$(1$ point$)$

${\displaystyle \underset{6}{\overset{8}{}}}23x^{2}dx$

a$)$ Approximate the definite integral with the Trapezoid Rule and $n=4.$

$$

b$)$ Approximate the definite integral with Simpson's Rule and $n=4.$

$$

c$)$ Find the exact value of the integral.

$$

Note: You can earn partial credit on this problem.