Why don't I have to put the +C after my answer for a definite integral?

When you evaluate a definite integral, we can think about using the "+C" and see what happens. Let's take (INT)2x dx between 2 and 3. We then have [x²+C] between 2 and 3. For x=3 we have 9+C, and for x=2 we have 4+C. To evaluate the integral we subtract the lower limit from the upper one so we have (INT)2x dx = (9+C) - (4+C)  =9+C-4-C  =5. So generally, we can say that when we evaluate a definite integral, the constant terms cancel out so we don't usually bother to write them down.