Trapezoidal rule

Create a MATLAB function $[$DLV$]$integrateTrap$(),$ which takes and integrates an input function using the trapezoidal rule.

$$ The input arguments are: a function, the step width h$,$ lower bound, and

upper bound of the integration interval, in that order $(4$ total$).$

$$ The output of the function is the integral of the input function between the

lower bound and the upper bound.

Use this MATLAB function to numerically calculate the integral of the function f$($x$)=$ e$^(2*$x$)$ across the interval $[-5,5]$ with step widths h $=0\mathrm{.}1,0\mathrm{.}01,$ and $0\mathrm{.}001.$ Plot the following in GnuPlot $[$DLV$]$:

$$ The input function $($e$^2$x$)$ across the interval;

$$ The numerical integral values $($calculated in MATLAB$)$ in form of a bar

graph for each step width h together with the analytical integral value

also as a bar graph next to each numerical integral bar graph.

$$ Make the plot look as clean as you can: give it a legend and ensure that the numerical integral bar graphs have a different color than the

analytical integral bar graphs.

$2)$ SimpsonRule

Create another MATLAB function $[$DLV$]$integrateSimpson$()$ just as in $1),$ which takes the same input arguments. Create the same plot required in question $1)[$DLV$]$ for the $3$ step widths h