Why do I need to add the + C when finding an indefinite integral?

When you differenciate a function, the constant term turns to 0. So a lot of different functions like x² + 7 and x² - 3 will have the same derivative, this means that going from the derivative to the original function we can only get the non constant terms right and therefore we must add a + C. If the integral is definite then we don't need the + C because by evaluating the difference when plugging the limits, we get F(top limit) + C - (F(bottom limit) + C) = F(top) - F(bottom) where F(x) is the integrated function.