We now have a way of evaluating this definite integral. Conceptually, we knew that this is the exact change in position between a and b, but we already figured out a way to figure out the exact change in position between a and b. So let me write all this down. We have that the definite integral between a and b of v of t dt is equal to s of b minus s of a, where s of t is the anti-derivative of v of t. And this notion, although I've written in a very nontraditional used position velocity, this is the second fundamental theorem of calculus. And you're probably wondering about the first. We'll talk about that in another video. But this is a super useful way of evaluating definite integrals and finding the area under a curve.