Two numerical methods for finding the area under a curve are the trapezium rule, where the area is split into trapezia, and the rectangle rule where you split into rectangles. The rectangle rule has two forms, one where you take the height at the midpoint and one where you take the height of the vertex on the left. Given the area is split into the same number of smaller shapes, is there ever going to be a case when the rectangles are better than trapezia? I can't think of one! But there must be a case where rectangles are better, or why bother learning the method?