Examples of quantum integrals

We first consider a method of centering and a change of variable formula for a quantum integral. We then present three types of quantum integrals. The first considers the expectation of the number of heads in $n$ flips of a "quantum coin". The next computes quantum integrals for destructive pairs examples. The last computes quantum integrals for a (Lebesgue)^2 quantum measure. For this last type we prove some quantum counterparts of the fundamental theorem of calculus.