Homework Help: A question about Upper Darboux Integrals

1. Dec 5, 2012

Artusartos

http://math.berkeley.edu/~scanez/courses/math104/fall11/homework/hw10-solns.pdf

For qustion 32.6, I'm not sure if I'm understanding how there can be a "sequence" of upper and lower darboux integrals.

So (for example), what is the difference between $$U_{10}$$ and $$U_{11}$$? Does it mean that $$U_{10}$$ is the upper darboux integral when there are 10 partitions (10 rectangles)...and $$U_{11}$$ is the upper darboux integral when there are 11 partitions? So, if we have $$U_1$$, does it mean that there is only one partition (so only one rectangle)?