So if we just multiply the height times the base, that this is going to be equal to the area under the curve, which is the definite integral from x to x plus delta x, x to x plus delta x of f of t dt. This is what the mean value theorem of integrals tells us. If f is a continuous function, there exists a c in this interval between our two endpoints, where the function evaluated at the c is essentially, you can view it as the mean height. And if you take that mean value of the function and you multiply it times the base, you're going to get the area of the curve. Or another way of rewriting this, you could say that f of c, there exists a c in that interval where f of c is equal to 1 over delta x. I'm just dividing both sides by delta x, times the definite integral from x to x plus delta x of f of t dt. And this is often viewed as the mean value of the function over the interval. Why is that?