Let $a$ be a postive real number. If $f$ is a continious and even function defined on the interval $[-a,a]$, then find the value of $$\int_{-a}^{a} \frac{f(x)} {1+e^x} dx. $$
My answer is :
$$2 \int_{0}^{a} \frac{f(x)} {1+e^x} dx $$ because $\int_{-a}^{a} = 2\int_{0}^{a}$.
Is it correct??
any hints/solution will be appreciated