Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 4 of x squared, dx

Answer 1

it's clearly true, since the area of a trapezoid is the average of the two surrounding rectangles.
A = (b1 + b2)/2 * h

Now just do the tedious math to show it in this case