ABSTRACT
In this chapter, the author knows quite a bit about the Riemann - Stieltjes integral in theory. However, he does not know how to compute a Riemann - Stieltjes integral and the author only knows that Riemann - Stieltjes integrals exist for a few types of integrators: those that are bounded with a finite number of jumps and the identity integrator. As readers might expect, the author proves a Riemann - Stieltjes variant of the Fundamental Theorem of Calculus. He begins by looking at continuous integrands. The function is everywhere continuous from the right and represents the probability of rolling a number. It is called the cumulative probability distribution function of a fair pair of dice.
