Combining Definite Integrals on Adjacent Intervals

There is a special property concerning the combination of definite integrals with the same integrand. Generically, it is as follows:

$\int^{b}_{a}f(x)dx + \int^{c}_{b}f(x)dx = \int^{c}_{a}f(x)dx$

In this case, $a$, $b$, and $c$ are real numbers. It is important that the three integrands are the same function.

Note that the same formula can be used to break up one definite integral into two with the same integrand. Just apply the formula above backwards.