I would like to simplify the following Riemann–Stieltjes integral:
$$h(t) = \int_{0}^{1/t}f(u)\times dg^{(n)}\left(\frac{1}{u}\right)$$
with
$$dg^{(n)}\left(\frac{1}{u}\right) = \left(\frac{d^ng(x)}{dx}\right)_{x=1/u}$$
and obtain the equivalent Riemann integral:
$$h(t) = \int_{0}^{1/t}F\left[f(u), g^{(n+1)}\left(\frac{1}{u}\right)\right]\times du$$
My major concern is how to transform the $dg^{(n)}\left(1/u\right)$, assuming that $g$ is continuous. Any reference about practical calculations of the Riemann–Stieltjes integral would also be greatly appreciated as it is not my academic background and such calculations are for engineering purpose.