E1: Start with the default setting: x1 = 1; x2 = 4; n = 10.
Verify that both graphs really limit the intervals in the y direction by the highest, respectively the lowest value in the interval (observe the sign of the function itself!). Consider the systematic deviation of the sum from the analytic solution.
E2: Compare the construction with the classical rectangle (step) algorithm.
E4: Increase n and observe the process of convergence to the limit value as the interval width decreases.
E4: Draw the end point at a large number for n and observe how the intervals limit lines "paint" the area under the curve. You will not visibly recognize a difference between sum and integral.
E5: Change the initial point with the slider. Draw the end point beyond the initial point and control if the result is still correct.