$\int\limits_{π/2}^{-π/2}\frac{\cos x}{1+e^x}dx$ is equal to:

1 2 -1 -2

-1

$I=\int\limits_{π/2}^{-π/2}\frac{\cos x}{1+e^x}dx=\int\limits_{0}^{π/2}(\frac{\cos x}{1+e^x}+\frac{\cos (-x)}{1+e^{-x}})dx=\int\limits_{0}^{π/2}\cos x(\frac{1+e^x}{1+e^x})dx=\int\limits_{0}^{π/2}\cos x\,dx=-1$