Question $1.$ Write two Matlab functions $S13(F,h)$ and $S38(F,h)$ that calculate the approximate integral given the vector of values $F$ and the uniform spacing of nodes $h.$ As the name suggeste, the first should use the Simpson composite $\frac{1}{3}$ rule and the second the Simpson composite $\frac{3}{8}$ rule. Depending on the number of sampled points $($the length $N$ of the vector $F)$ it may not be possible to evenly divide the integration interval. For example, if $N=5,$ then there are $4$ segments and you can fit exactly two subintervals using the $\frac{1}{3}$ rule, but only one subinterval with $\frac{3}{8}$ plus an extra segment. In the latter case, zero$-$pads the input vector $F$ until you have the right number of point. In the example above, you will need to add two more zeros at the end of $F.$ Similarly, if you have $N=10,$ then you have $3$ subintervals with $3$ segments each, so the $\frac{3}{8}$ method is fine, but you will need to zero$-$pad $F$ with one extra point to fit $5$ subintervals for the $\frac{1}{3}$ method. In your code, do NOT use for or while loops. Use instead slicing and the builtin Matlab function sum if you need to add the elements of an array. It is ok to use a for or while loop to zero$-$pad.