2．极限 $\displaystyle{\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{n}{n^{2}+i^{2}}}$ 可以通过下面哪个积分计算？ ．
A
$\displaystyle{\int_{0}^{1} \frac{x}{x^{2}+1} \mathrm{~d} x}$
B
$\displaystyle{\int_{0}^{1} \frac{1}{1+x^{2}} \mathrm{~d} x}$
C
$\displaystyle{\int_{0}^{+\infty} \frac{x}{x^{2}+1} \mathrm{~d} x}$
D
$\displaystyle \int_{0}^{+\infty} \frac{1}{1+x^{2}} \mathrm{~d} x$