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Integral equations of the form $$ x(t)=x(t_0)+\int_{t_0}^td[A]\,x=f(t)-f(t_0)$$ are natural generalizations of systems of lineardifferential equations. Their main goal is that they admit solutions which neednot be absolutely continuous. Up to now such equations have been considered byseveral authors starting with J. Kurzweil and T.H. Hildebrandt. These authorsworked with several different concepts of the Stieltjes type integral likeYoung's (Hildebrandt), Kurzweil's (Kurzweil, Schwabik and Tvrd\'{y}), Dushnik's(H\"{o}nig) or Lebesgue's (Ashordia, Meng and Zhang). Thus an interestingquestion arises: what are the relationships between all these concepts?  Our aim is to give an answer to this question. In addition, we present alsoconvergence results that are new for the Young and Dushnik integrals. Let usemphasize that the proofs of all the assertions presented in this paper arebased on rather elementary tools.

On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil