Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a non-zero even function such that
$\int_{-1}^1 f(x) d x=\alpha$
Then, the value of the integral
$\int_{-1}^1 \frac{f(x)}{1+e^x} d x$ is

• A

  $\alpha$.
• B

  $\alpha e^{-\alpha}$.
• Correct answer
  C

  $\frac{\alpha}{2}$.
• D

  $\frac{e^{-\alpha}}{2}$.

Hence, the correct answer is option: 'C'.