Problem $1$

Write a C program that uses the rectangular rule, trapezoidal rule, and Simpson's rule to numerically calculate the following definite integral:

${\displaystyle \underset{1}{\overset{3}{}}}\sqrt[\phantom{2}]{-x^2+4x-3}dx$

The number of partitions should be input by the user $($needs to be even$).$ Print the results for all three methods to the screen.

You can check the correctness of your answer by plotting the function being integrated, $\sqrt[\phantom{2}]{-x^2+4x-3},$ and calculating the area under the curve by hand. Submit the gnuplot script you use to generate this plot.