Evaluating $\int_{-a}^a \frac{f(x)+1}{b^x+1}\,\mathrm dx$ for a $y$-axis symmetrical function $f$
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even