Consider the function, $f(x)=(x^2-6),$ bounded on the interval $0,4.$

a$.(5$pts$)$ Estimate the value of ${\displaystyle \underset{0}{\overset{4}{}}}(x^2-6)dx$ using Riemann sums with $100$ equally spaced sub$-$intervals using right hand end points. Hint: I recommend doing this using $n$ equally spaced sub$-$intervals in your work, then using $n=100$ in the final step.

b$.($lpt$)$ Find the exact value of ${\displaystyle \underset{0}{\overset{4}{}}}(x^2-6)dx$ using Riemann sums and limits$.($Don$\text{'}$t repeat all the work from part a$!$ but don't use the Fundamental Theorem of calculus either!$)$