We have already covered the notion of area between a curve and the x-axis using a definite integral. We are now going to then extend this to think about the area between curves. So let's say we care about the region from x equals a to x equals b between y equals f of x and y is equal to g of x. So that would be this area right over here. So based on what you already know about definite integrals, how would you actually try to calculate this? Well, one natural thing that you might say is, well, look, if I were to take the integral from a to b of f of x dx, that would give me the entire area below f of x and above the x-axis, and then if I were to subtract from that, if I were to subtract from that this area right over here, which is equal to, that's the definite integral from a to b of g of x dx, well, then I would net out with the original area that I cared about. I would net out with this area right over here, and that indeed would be the case, and we know from our integration properties that we can rewrite this as the integral from a to b of, let me put some parentheses here, of f of x minus g of x, minus g of x dx, and now I will make a claim to you, and we'll build a little bit more intuition for this as we go through this video, but over an interval from a to b where f of x is greater than g of x, like this interval right over here, this is always going to be the case, that the area between the curves is going to be the integral for the x interval that we care about from a to b of f of x minus g of x, so I know what you're thinking.