Question

Approximate the area of the region bounded by the graph of f(t) = (t/2 - pi/8) and the t-axis on [0,pi] with n = 4 sub intervals to determine the height of each rectangle.

The approximate area of the region is:

Round to two decimal places as needed

Answer 1

with 4 equal subintervals, the width of each is π/4.
The area of each rectangle is, as usual, width * height, but if you want the geometric area (not the algebraic area), then since the 1st interval is below the t-axis, you need to subtract its area.
If you want to use left-side approximations, then that makes the area
π/4 (-f(0) + f(π/4) + f(π/2) + f(3π/4))
Using right-side rectangles, you get
π/4 (-f(π/4) + f(π/2) + f(3π/4) + f(π))
and if you want midpoint approximations, you need
π/4 (-f(π/8) + f(3π/8) + f(5π/8) + f(7π/8))

I hope you see how important it is to be specific in your questions.