not the best pic, but look at this
blue is left
red is right
green is mid

so what you are doing is finding the area of each one of those rectangles and adding them up to approximate the area created from the equation and the x-axis

since the equation is symmetric over the interval you can see that both the right side and left side approaches will give the same answer, and also one rectangle will have 0 area, since the point lies on the x-axis
the midpoint approach works better here because of this