$\lim \limits_{n \to \infty} \sum \limits_{k=1}^m \large\frac{k}{n^2+k^2}$ is equal to

Question

$\begin{array}{1 1} (1/2) \log 2 \\ \log 2 \\\large\frac{\pi}{4} \\\large \frac{\pi}{2} \end{array} $