A Remark on the Existence of Riemann-Stieltjes Integral

Here Riemann-Stieltjes(R-S)integral is concerned with.As it is well-known,this type of integral is an important generalization to Riemann integral.Our purpose is to investigate of R-S integrality and give a new proof of the theorem by introducing some properties of bounded variation function.As a result,we establish the sufficient and necessary conditions of the existence theorem of R-S integral.Since class period is limited in the university calculus course,there is some substantial difficulty on teaching and studying such topic.The students of mathematics department may not understand the conceptions on R-S integral well.So our work will be helpful to them and all who are interested in the topic.