I wish to write code for Riemann-Stieltjes integrals in Mathematica.
A necessary condition for the theorem to hold is that the function must be continuous. The domain of the function is a closed real interval containing infinitely many points, so I can't check continuity at each and every point.
I wish to know if there are any built-in functions in Mathematica that determine if a function is continuous or not. Or if there is any function that returns point of singularities of function?