Limit of Definite Integral #1

$\large I_n =\int_0^1 \frac{x^n}{x^2 + a^2} \, dx$

Define the integral $I_n$ as above for positive real variable $a$ independent of $x$ and natural number $n$ . Evaluate the limit below.

$\large \lim_{n\to\infty} \left [ \sqrt n \left( n I_n - \frac1{a^2+1} \right) \right ]$