Strip sums by computer

You will write three small functions that add up strips under a curve: one with the height at the left end of each strip, one with the right end and one with the middle. The checker tests them on a parabola and on a line.

The idea. Cut $[a, b]$ into $n$ strips of width $h = \dfrac{b - a}{n}$. The strip $i$, counted from $0$, runs from $a + ih$ to $a + (i + 1)h$. Its area is the height times $h$. The sum of all the strips estimates the area under the curve.

Your tasks.

1. Finish left_sum(f, a, b, n). Use the height at the left end of each strip.
2. Finish right_sum(f, a, b, n). Use the height at the right end of each strip.
3. Finish midpoint_sum(f, a, b, n). Use the height at the middle of each strip.