By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_0^1x\;(1-x)^n\;dx \end{align*}$

Question

$\begin{array}{1 1} \frac{1}{(n+1)(n+2)} \\ \frac{1}{(n-1)(n-2)} \\ \frac{n+1}{n+2} \\ \frac{n}{(n+1)(n+2)} \end{array}$