I'm a calculus tutor at Boise State, and integrals are probably one of my favorite things to help with. I just love how it's such a large stepping stone for calculus. You start with the derivative, which I would like to make another page for in the future, which defines the instantaneous rate of change at a single point on a line. Then, you find the area of that line with the integral. But it's interesting because they build off of each other and yet are inverses of each other. I hate calling it an antiderivative though. You're also able to find the area under a curve with Riemann sums, and I LOVE Riemann Sums, my other favorite thing to help with when tutoring... noticing a pattern here. However, they aren't as accurate as integrals, it's more of an approximation, or an educated guess, you could say.

An interesting topic on this concept is integrability of functions. How to know if a function is integrable. Well its easy, if the function is contiuous on a given interval, there you go. But also, if there is only a finite number of discontinuities on an interval.. what? Well, here's the cool thing. Functions with sharp turns such as absolute value functions aren't differentiable, but they are integrable! $y=|x|$ is integrable for all values of $x$, but you can't take the derivative of that. So, I guess it's not TOTALLY an inverse of derivatives, because the set of differentiable functions is a subset of integrable functions.