By integrating round the contour involving the real axis and the line $\operatorname{Im}(z)=2 \pi$, or otherwise, evaluate

$$\int_{-\infty}^{\infty} \frac{e^{a x}}{1+e^{x}} d x, \quad 0<a<1 .$$

Explain why the given restriction on the value $a$ is necessary.