b$)$ Evaluate the following integral:

${\displaystyle \underset{-2}{\overset{4}{}}}(1-x-4x^3+3x^5)dx$

$($i$)$ Analytically

$($ii$)$ Single operation of the trapezoidal rule

$($iii$)$ Trapezoidal rule with $n=2$ and $4$

$($iv$)$ Single application of Simpson's $\frac{1}{3}$ rule

$($v$)$ Simpson's $\frac{3}{8}$ rule

For each of the numerical estimates $($ii$)$ to $($v$),$ determine the percent relative error based on $($i$).$