$1.($a$)$ Use the Midpoint Rule with $n=4$ subintervals to estimate ${\displaystyle \underset{0}{\overset{2}{}}}{x}^{2}dx.$

$($b$)$ Compute the integral exactly.

$2.$ For the integral of problem #$1$ :

$($a$)$ Use the Error Bound to find the bound for the error.

$($b$)$ Compute the error made when using this estimate.

$($QUESTION $2$ ONLY$)$