sequences and series - What is$sum_{n=1}^inftyfrac{1}{n^2+1}$?

What is

$$\sum_{n=1}^\infty\frac{1}{n^2+1}$$
I know that
$\sum_{n=1}^\infty\frac1{n^2}=\frac{\pi^2}6$ but what about if we add a one to it in the denominator, can we still figure it out?