Numerical Integration

$9\mathrm{.}31.$ Consider the integral ${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\frac{dx}{1+si{n}^2(x)}.$

$($a$)$ Approximate this integral numerically using the trapezoidal rule and $N=4.$

$($b$)$ Approximate this integral numerically using Simpson's rule and $N=4.$