They, once again, they are all just shifted up and down by this f of x function, but these are the exact same rectangles, or they have the exact same heights. And the limit as you get more and more of these by making them thinner and thinner is going to be the same as the limit as you get more and more of these as you get thinner and thinner. And so this area right over here, and I'm obviously not doing a rigorous proof, I'm giving you the intuition for it, is the exact same thing as this area right over here. So the area under this curve, the definite integral from a to b of f of x plus g of x dx, is just going to be the sum of these two, is just going to be the sum of these two definite integrals. And you might say, oh, this is obvious, or maybe it's not so obvious, but when is this actually useful? Well, as you later actually learn to evaluate these integrals, you'll see that one of the most powerful ideas is being able to decompose them in this way, to say, okay, if I'm taking the definite integral from zero to one of x squared plus sine of x, which you may or may not have learned to do so far, you can at least start to break this down. You can say, okay, well, this is going to be the same thing as the integral from zero to one of x squared dx, plus the integral from zero to one of sine of x dx.