In deriving the trapezoidal method for solving the differential equation y′ = f(t,y) we integrated the equation over the interval t_j ≤ t ≤ t_j+1. In this problem you are to integrate the equation over the interval t_j−1 ≤ t ≤ t_j+1.

(a) What numerical method is obtained if Simpson’s rule is used on the resulting integral? What is the truncation error for this rule?

(b) What numerical method is obtained if the midpoint rule is used on the resulting integral? What is the truncation error for this rule?