We're summing up the infinite number of those infinitely thin rectangles or the areas of those infinitely thin rectangles between 1 and 4. So that's where the notation of the definite integral comes from. But we still haven't done anything. We've just written some notation that says the exact area between 1 and 4 under the curve f of x and above the x-axis. In order to actually do anything really productive with this, we have to turn to the second fundamental theorem of calculus, sometimes called part 2 of the fundamental theorem of calculus, which tells us that if f has an antiderivative, so if we have the antiderivative of f, so f of x is derivative of some function capital F of x, or another way of saying it is capital F of x is the antiderivative of lowercase f of x, then I can evaluate this thing, and we do a whole video on conceptually understanding why this makes sense, we can evaluate this by evaluating the antiderivative of f or an antiderivative of f at 4 and from that subtract the antiderivative evaluated at 1. So let's do it for this particular case right over here. So we are taking, I'll just rewrite this statement, instead of writing f of x I'll write x squared, so the definite integral from 1 to 4 of x squared dx, well, we're just going to have to figure out what the antiderivative is.