Answer:
a. Simpson method

b. Trapezoid method

Midpoint method

Explanation:
a. We want to compute
using five point Simpson’s method.
The Simpson's rule states that

where

We know that a = −1, b = 1, n = 4.
Therefore,
.
Divide the interval [−1,1] into n = 4 sub-intervals of length


Now, we just evaluate the function at these endpoints:





Finally, just sum up the above values and multiply by

.
b.
The trapezoidal rule states that

where

We know that a = −1, b = 1, n = 5.
Therefore,
.
Divide the interval [−1,1] into n = 5 sub-intervals of length


Now, we just evaluate the function at these endpoints:







The Midpoint method uses the midpoints of sub-interval:

where

We know that a = −1, b = 1, n = 5.
Therefore,
.
Divide the interval [−1,1] into n = 5 sub-intervals of length


Now, we just evaluate the function at these endpoints:





