How to find $\lim_{n\rightarrow \infty} \frac {n^2}{n^3+n +1} + \frac {n^2}{n^3 +n +2} +.....+\frac {n^2}{n^3 + 2n}$? 
How to find 
  $$
\lim_{n\rightarrow \infty} \frac {n^2}{n^3+n +1} + \frac {n^2}{n^3 +n +2} +.....+\frac {n^2}{n^3 + 2n}?
$$

I was thinking about the Riemann sum, but I am not able to do it. 

\begin{align*}
\sum_{k=1}^{n}\dfrac{n^{2}}{n^{3}+n+k}\leq\sum_{k=1}^{n}\dfrac{n^{2}}{n^{3}+n+1}=\dfrac{n^{3}}{n^{3}+n+1}
\end{align*}
and
\begin{align*}
\sum_{k=1}^{n}\dfrac{n^{2}}{n^{3}+n+k}\geq\sum_{k=1}^{n}\dfrac{n^{2}}{n^{3}+n+n}=\dfrac{n^{3}}{n^{3}+2n},
\end{align*}
now use Squeeze Theorem to conclude.
