Here, you can see a function with its lower sum and upper sum on the interval [a, b].

Drag the endpoints a and b of the interval with the mouse. What characteristics of the rectangles of the (a) lower sum, (b) upper sum do you see? Write down your observations.

Now, change the number of rectangles n by moving the slider with the mouse. How does this affect the difference between lower and upper sum? Write down your conjectures.

Do your conjectures of (2) hold for other intervals [a, b]? Check this by changing both the interval end points and the number of rectangles.