The Riemann-Stieltjes integral is a generalization of the Riemann integral. Instead of dealing with just one function f (integrand), it deals with two functions f (integrand) and g (integrator). In what follows we will assume that all functions are defined on the interval [a, b] and are bounded. We will begin with the assumption that the function g is nondecreasing, but later consider the general function. In this chapter, we will use the same notations of Chapter 19.