Situation $1$: Evaluate the following integral $(20$ points$)$:

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

$1$a$)$ What is the integral value using analytical methods? $($Exact answer, no tolerance$)$

$1$b$)$ What is the integral value using the single application trapezoidal rule? $($Exact answer, no tolerance$)$

$1$c$)$ What is the integral value using the single application Simpson's $1/3$ rule? $($Exact answer, no tolerance$)$

$1$d$)$ What is the integral value using the single application Simpson's $3/8$ rule? $($Exact answer, no tolerance$)$