Problem $8.$ Use a right$-$hand Riemann sum with $n$ equal subdivisions, then take a limit as $n,$ to compute the exact value of

${\displaystyle \underset{0}{\overset{1}{}}}xdx$

Hint: This sum formula may be useful:

${\displaystyle \underset{i=1}{\overset{n}{}}}i=\frac{n(n+1)}{2}$