I was given the problem: find the area of the region bounded by $y=1/x$, $y=x^2$, $y=0$, and $x=e$.
My approach was to break it up into two integrals, $\displaystyle \int_0^1 (x^2-0)\,dx$ and $\displaystyle \int_1^e\left(\frac{1}{x}-0\right)\,dx$.
Doing it this way resulted in an answer of 4/3. Simply by eyeballing it, the result seems reasonable, but I was wondering if there was a way to double check, or if someone else could verify that I am either doing this correctly or incorrectly.