Definite Integral of Even Function/Corollary

Corollary to Definite Integral of Even Function
Let $f$ be an even function with a primitive on the open interval $\left({-a \,.\,.\, a}\right)$, where $a > 0$.

Then the improper integral of $f$ on $\left({-a \,.\,.\, a}\right)$ is:
 * $\displaystyle \int_{\mathop \to -a}^{\mathop \to a} f \left({x}\right) \rd x = 2 \int_0^{\mathop \to a} f \left({x}\right) \rd x$