Let's say we've got some function f that is continuous over the interval between c and d. And the reason why I'm using c and d instead of a and b is so I can use a and b for later. And let's say we set up some function capital F of x, which is defined as the area under the curve between c and some value x, where x is in this interval where f is continuous, under the curve, so it's the area under the curve between c and x. So if this is x right over here, under the curve, f of t, dt. So this right over here, f of x, is that area. That right over there is what f of x is. Now the fundamental theorem of calculus tells us that if f is continuous over this interval, then f of x is differentiable at every x in the interval and the derivative, the derivative of capital F of x. And let me be clear.