could someone explain how to solve problems like this one. an explanation would be more helpful than just an answer, thanks.
find the area between the curves y=cosx and the x axis bound by the lines x=0 and x=pi.
The integral of a function $\displaystyle f$ between two given points $\displaystyle a$ and $\displaystyle b$ gives you the "area" (apart from possibly a minus sign) between the graph of $\displaystyle f$ and the $\displaystyle x$ axis, bounded by the lines $\displaystyle x=a$ and $\displaystyle x=b$.
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 $\displaystyle \cos (x)$, bounded by the lines $\displaystyle x=0$ and $\displaystyle x=\pi$. First observe that, between $\displaystyle 0$ and $\displaystyle \pi$, $\displaystyle \cos (x)\geq 0$. So all you have to do is integrate $\displaystyle \cos (x)$ with $\displaystyle x$ running from $\displaystyle 0$ to $\displaystyle \pi$.
Edit: huge mistake from my part (was picturing $\displaystyle \sin (x)$ in my head instead of cosine). Obviously $\displaystyle \cos (x) \leq 0$ for $\displaystyle x\in [\frac{\pi}{2},\pi]$. I'm terribly sorry. The post below me says what needs to be said