Problem $1(20$ points$)$:

Estimate the following integral using specified method. Do not compute the integral

analytically.

$I(f)={\displaystyle \underset{0}{\overset{1}{}}}{e}^{-x}dx$

$($a$)$ Use improved trapezoid rule with a grid spacing $h=0\mathrm{.}2.$

$($b$)$ Use Simpson's rules with a grid spacing $h=0\mathrm{.}2.$ Keep in mind that you want the

estimate to be as accurate as possible. Justify your choice of the integration formulas.