you sure? I took a World Religion course and we covered Islam. Never found that part. Not saying it wasn't there but if it was, we never covered it.
Such claims are taken from a partial quote of Sura 9, Verse 5 ...
Which, as always, requires some context...
Sura 9 addressed the circumstances for defending the minority Muslim community which was under attack from the Arab tribes seeking their destruction despite a previous agreement for peace and sharing pilgrimage rights. It requires the muslims to strike/kill the polytheist Arab tribes until the aggression/genocide against them stopped, and explained under which conditions a specific peace treaty had to be adhered to, and ultimately dissolved the conditions of the treaty at its term's end. These specific circumstance verses occur often in the Quran.
For context see the surrounding verses, including full text of verse 5:
...
9:1
[This is a declaration of] disassociation, from Allah and His Messenger, to those with whom you had made a treaty among the polytheists.
9:2
So travel freely, [O disbelievers] throughout the land [during] four months but know that you cannot cause failure to Allah and that Allah will disgrace the disbelievers.
9:3
And [it is] an announcement from Allah and His Messenger to the people on the day of the greater pilgrimage that Allah is disassociated from the disbelievers, and [so is] His Messenger. So if you repent, that is best for you; but if you turn away – then know that you will not cause failure to Allah. And give tidings to those who disbelieve of a painful punishment.
9:4
Excepted are those with whom you made a treaty among the polytheists and then they have not been deficient toward you in anything or supported anyone against you; so complete for them their treaty until their term [has ended]. Indeed, Allah loves the righteous [who fear Him].
9:5
And when the sacred months have passed, then kill the polytheists wherever you find them and capture them and besiege them and sit in wait for them at every place of ambush. But if they should repent, establish prayer, and give zakah, let them [go] on their way. Indeed, Allah is Forgiving and Merciful.
9:6
And if any one of the polytheists seeks your protection, then grant him protection so that he may hear the words of Allah. Then deliver him to his place of safety. That is because they are a people who do not know.
...
Although the Quran is very hostile in rhetoric towards 'the non-believers' (polytheists and atheists: damning to the hell fire, eternal punishment in the afterlife, etc.), it forbids being the aggressor and compulsion of religion. But it does require self-defense and defense of fellow muslims under attack.
So... no, the Quran, taken in its context and in its totality, does not instruct its followers to go out and kill all unbelievers. Actually, it forbids such an act.
However, by not including the context of Sura 9:5, not quoting the verse in its totality, and not considering other verses which clarify the rules of war, it can be made to seem so.