Limit of Riemannian integrals with Lebesgue Show: $\lim\limits_{n\rightarrow\infty}\int_0^nx^i(1-\frac{x}{n})^ndx=i!$ for $i\geq 0$.


Hello there. Question is how do this? Which relation between Lebesgue and Riemann integrals must be used? Appreciate any hints. Thank you.
It should be
$$
0\lt\int_0^n x^i\left(1-\frac{x}{n}\right)^ndx\le
\int_0^n x^ie^{-x}dx\le\int_0^\infty x^ie^{-x}dx=\Gamma(i+1)=i!.
$$
It should be
$$
0\lt\int_0^n x^i\left(1-\frac{x}{n}\right)^ndx\le
\int_0^n x^ie^{-x}dx\le\int_0^\infty x^ie^{-x}dx=\Gamma(i+1)=i!.
$$