Riemann-Stieltjes Integration problem I have two functions $f$ and $g$ and I need to show that $f$ is Riemann-Stieltjes integrable with respect to $g$. I was able to calculate the integral, but I'm not sure how to actually prove why it is Riemann-Stieltjes integrable.
Let
\begin{align*}
f(x) &=x^2 \qquad x \in [0,5]\\
\\
g(x) &=\left\{ 
\begin{array}{ll} 
0 & \textrm{if }0 \leq x<2 \\
 p & \textrm{if } 2 \leq x<4 \\
 1 & \textrm{if } 4 \leq x \leq 5
\end{array} \right.
\end{align*}
After calculating the integral I got it equal to $16-12p$. Now how do I go about actually proving this? Or have I already done so?

Because $f$ is continuous, it is sufficient to show that $g$ is of bounded variation (equivalently: $g$ is the difference of two monotone functions).
