That if I found a c that is in this interval, that it's greater than or equal to a and it's less than or equal to b, why is it useful to be able to break up the integral this way? Well, as you'll see, this is really useful. It can be very useful when you're looking at functions that have discontinuities. If they have step functions, you can break up the larger integral into smaller integrals. You'll also see that this is useful when we prove the fundamental theorem of calculus. So in general, this is actually a very, very, very useful technique. Let me actually draw an integral where it might be very useful to utilize that property.