That is, is it possible that but for some other than , or for some other than , but ? If it is, can you give me an example? Thanks.
Riemann integrability does not imply Riemann-Stieltjes integrability,
and Riemann-Stieltjes integrability does not imply Riemann integrability.
Rudin's book <<principle of mathematical analysis>> provide a execise as a example in the section on Riemann integral.