Evaluate the integral ${\displaystyle \underset{0}{\overset{1\mathrm{.}2}{}}}{e}^{x}dx,$ taking $n=5$ using Simpson's $\frac{1}{3}$ rule.

a$)$ Evaluate by hand using Simpson's Rule.

b$)$ Draw the flow chart expressing the algorithm for the solution.

c$)$ Create an $m-$script utilizing Simpson's $\frac{1}{3}$ rule to evaluate this integral.

i$.$ Write the MATLAB Code $(m-$script$)$ on the answer sheet.

ii$.$ Add explanation $($comment$)$ with $(\%)$ for each line of MATLAB Code.

iii. Build the $m-$script in MATLAB.

iv$.$ Run the $m-$script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard.