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Originally Posted by **cheloniophile** In what situations would a Riemann-Stieltjes integral be used rather than a Riemann integral? Are there any functions which are Riemann-Stieltjes integrable but not Riemann integrable? |

From the sound of your question, I don't think you appreciate the difference between R integral and R-S integral. The R integral involves integrating a given function. The R-S integral involves 2 functions that is the integral of one function with respect to a differential of another function. You would use whatever the particular problem calls for. They are not in any way interchangable, except in the trivial case where the second function for the R-S integral is F(x)=kx.