$19\mathrm{.}4$ Evaluate the following integral:

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

$($a$)$ analytically, $($b$)$ single application of the trapezoidal rule, $($c$)$ composite trapezoidal rule with $n=2$ and $4,($d$)$ single application of Simpson's $\frac{1}{3}$ rule, $($e$)$ Simpson's $\frac{3}{8}$ rule, and $($f$)$ Boole's rule. For each of the numerical estimates $($b$)$ through $($f$),$ determine the true percent relative error based on $($a$).$