If we define Islam, not as the practice of Muslims, but as the teachings of Muhammad then violence is an integral part of Islam.
Those Muslims who teach that surah 9 of the Quran has not been abrogated (the final teaching of Muhammad), still affirm the command to disavow all treaties with polytheists and to subjugate Jews and Christians so that Islam may "prevail over every faith." This final surah of the Quran gives no limits to assimilation, subjugation and violence against non-Muslims. According to this surah those Muslims who do not fight are even counted among the hypocrites.
Former Muslim Nabeel Qureshi says,
"...frustrated by the increasing frequency and scale of Islamist terrorism [many people] suggest that Islam needs a reformation. What they may not realize is that radical Islam is the Islamic Reformation.
This might sound shocking, but consider: Just as the Protestant Reformation was an attempt to raze centuries of Catholic tradition and return to the canonical texts, so radical Islam is an attempt to raze centuries of traditions of various schools of Islamic thought and return to the canonical texts of the Quran and Muhammad's life.
The question arises then, If Muhammad taught this, why don't all Muslims believe this then? Because each persons Islam is interpreted through the tradition of their local imam or jurist. Many local imams may claim this part of the Quran has been abrogated. But those Muslims who continue to affirm surah 9 and the traditions of Muhammad and the earliest followers of Muhammad, believe violence or subjugation against non- Muslims is still valid. Qureshi says,
" the reason Muslims can be both devout and peaceful in spite of violent teachings in the Quran and hadith is that Muslim authorities have interpreted Islam in this manner for them, often in accordance with various schools of thought and centuries of accredited Islamic tradition. When Muslims wish to return to the roots of their faith, whether due to disillusionment with current expressions of Islam or a desire to please Allah and win his favor, violent expressions of Islam are often the result."
Qureshi continues,
"The radical Muslim emphasis on foundational texts and their disregard for centuries of Islamic tradition tend to resonate with Protestant sensibilities. In fact, Protestants often ask me if peaceful Muslims are "good Muslims" in light of the violent trajectory of the Quran and Muhammad's life. ... Muslims can legitimately practice peaceful forms of Islam. Outside of the Protestant "Scripture alone" perspective, most religions impute some authority to persons, and obedience to those authorities is part of the faith. Just as a "good Catholic" is one who obeys the Pope and adheres to the traditions of the Catholic Church, so a "good Muslim" is one who obeys his or her teachers and adheres to the traditions handed down in the practice of Islam ... perhaps the question Protestants intended to ask is whether an insistence upon peace is consistent with the foundations and origins of the Islamic faith. I have attempted to address that question head-on in this book: No, it is not.Muhammad engaged in many battles, both offensive and defensive, both provoked and unprovoked, leading the Muslim community in eighty-six raids and battles during the last nine years of his life. The Quran's final commands are found in surah 9, chronologically the last major chapter of the Quran, and they are the most violent commands of all. The name of the chapter, "al-Barra," means "the Disavowal." Not only was the surah a disavowal of peace treaties, but in many classic interpretations of Islam it was also a disavowal of other peaceful verses in the Quran through abrogation...These Quaranic teachings launched Muslims into world conquest and domination, and Muslims insistent on peace today must either ignore or reinvent whole swaths of Islamic history and thirteen centuries of Islamic tradition to dissociate themselves from violent Islam....Many peaceful Muslims do not do so consistently, instead simply ignoring some traditions as if they did not exist. In that case, though they may still be "good Muslims," they are not being consistent thinkers ...[so] the common assertion that violent Muslims are not truly Muslim is uninformed or even disingenuous....
...Al-Qaida, ISIS, and Boko Haram ... see themselves as champions of true Islam...Their practice of Islam places relatively greater emphasis on the foundational texts of the faith than does the practice of more moderate Muslims. Their methods are based on the writings of Sayyid Qutb, whose teachings were almost entirely derived from the Quran...When leaders and media members insist these groups are not Islamic, they are either speaking out of ignorance or intentionally engaging in propaganda. These groups are dynamic expressions of the modern Islamic reformation, and their interpretations of the Quran and hadith, in terms of being devoid of accreted tradition, are among the more pure in the Islamic world.
Excerpts from Answering Jihad by Nabeel Qureshi