$$f(x) = \frac{1}{e^x+e^{-x}}$$
$$I\_n=\int\_n^{n+1}f(x)dx\,\,\,\,\, n\in\mathbb N^\*$$
Show $f(n+1) \le I\_n \le f(n)$.  

I don't know what to do here. I realized that $I\_n$ can be calculated and also that $f(x)$ is decreasing but I still don't see the relation.  

$\int{f(x)dx}=\arctan e^x => I\_n=\arctan e^{n+1}-\arctan e^n$