On the relation between Denjoy--Khintchine and HK${}_r$-integrals

We locate Musial,&,Sagher’s concept of HK${}_r$-inte-gration within the approximate Henstock–Kurzweil integral theory. If to restrict HK${}_r$-integral by requirement that the indefinite HK${}_r$-integral is {\em continuous}, then it is included even in the classical Denjoy–Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper.