The integral $\int\limits_0^1 x(1-x)^{n} d x$ is equal to :

$\frac{1}{(n+2)(n+3)}$ $\frac{1}{(n+1)(n+2)}$ $\frac{1}{n(n+1)}$ $\frac{1}{(n-1)(n-2)}$

$\frac{1}{(n+1)(n+2)}$

The correct answer is Option (2) - $\frac{1}{(n+1)(n+2)}$