If we were to evaluate that integral from m to n of, let's put my dx here, of f of x minus, minus g of x, we already know from our integral properties, this is going to be equal to the integral from m to n of f of x dx minus the integral from m to n of g of x dx. Now let's think about what each of these represent. So this yellow integral right over here, that would give this, the negative of this area. So that would give a negative value here, but the magnitude of it, the absolute value of it, would be this area right over there. Now what would just the integral, I'm not even thinking about the negative sign here, what would the integral of this g of x of this blue integral give? Well, that would give this the negative of this entire area. But now we're gonna take the negative of that, and so this part right over here, this entire part, including this negative sign, would give us, would give us this entire area, the entire area.