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. You're like, okay, well, that worked when both of them were above the x-axis, but what about the case when f of x is above the x-axis and g of x is below the x-axis? So, for example, let's say that we were to think about this interval right over here. Let's say this is the point c, and that's x equals c. This is x equals d right over here, so what if we wanted to calculate this area that I am shading in right over here?