The integral of a function between two given points and gives you the "area" (apart from possibly a minus sign) between the graph of and the axis, bounded by the lines and .
If the function is nonnegative, there is no minus sign, so the integral is exactly the area beneath the curve.
You want to compute the are beneath the graph of , bounded by the lines and . First observe that, between and , . So all you have to do is integrate with running from to .
Edit: huge mistake from my part (was picturing in my head instead of cosine). Obviously for . I'm terribly sorry. The post below me says what needs to be said