Write the following limit of the Riemann sums as a definite integral

$($a$)$

$\underset{n}{lim}\frac{1}{n}[(3+\frac{1}{n}{)}^3+(3+\frac{2}{n}{)}^3+$cdots$+(3+\frac{n}{n}{)}^3]$

$($b$)$ By evaluating the definite integral from $(a),$ conclude the value of the limit$.$