$\lim _{n \rightarrow \infty} \sum_{i=1}^n \sum_{j=1}^n \frac{n}{(n+i)\left(n^2+j^2\right)}=$
A. $\int_0^1 \mathrm{~d} x \int_0^x \frac{1}{(1+x)\left(1+y^2\right)} \mathrm{d} y$.
B. $\int_0^1 \mathrm{~d} x \int_0^x \frac{1}{(1+x)(1+y)} \mathrm{d} y$.
C. $\int_0^1 \mathrm{~d} x \int_0^1 \frac{1}{(1+x)(1+y)} \mathrm{d} y$.
D. $\int_0^1 \mathrm{~d} x \int_0^1 \frac{1}{(1+x)\left(1+y^2\right)} \mathrm{d} y$.