The larger n is, the better an approximation it's going to be. So his definition of an integral, which is the actual area under the curve, or his definition of a definite integral, which is the actual area under a curve between a and b, is to take this Riemann sum, it doesn't have to be this one, take any Riemann sum, and take the limit as n approaches infinity. So just to be clear, what's happening when n approaches infinity? Let me draw another diagram here. So let's say that's my y-axis, this is my x-axis, this is my function. As n approaches infinity, so this is a, this is b, you're just going to have a ton of rectangles. You're just going to get a ton of rectangles over there and they're going to become better and better approximations for the actual area.