B$2.[8$ marks$]$ In this question we will compute the following definite integral

${\displaystyle \underset{0}{\overset{2}{}}}{x}^2+3xdx$

$($a$)$ Construct an approximation of ${\displaystyle \underset{0}{\overset{2}{}}}{x}^2+3xdx$ using a Riemann sum with $n$ rectangle using a right end approximation. Compute the closed form of your Riemann sum.

$($b$)$ Compute ${\displaystyle \underset{0}{\overset{2}{}}}{x}^2+3xdx$ by taking the limit of your solution in the previous part as $n$ approaches $.$

$($c$)$ Compute ${\displaystyle \underset{0}{\overset{2}{}}}{x}^2+3xdx$ using the Fundamental Theorem of Calculus II$.($Hint: your solution to this part should be the same as the previous part.