If you would like to explore more of the topics you have introduced then that are two classics that are standards:INTRODUCTION TO THE THEORY OF INTERGRATIONby T. H. Hildebrandt andTHEORY OF THE INTEGRALby Stanislaw Saks. I think that Hildebrandt is still the best on Riemann and Riemann-Stieltjes integrals there is. He also has a good discussion ofcontent of a setwhich was the subject of another one of your postings.

If you are interested in modern work in integration theory I would suggest Robert McLeod’s bookTHE GENERALIZIED RIEMANM INTEGRAL. It explores a relatively new definition of the integral that makes any derivative, F’(x), integrable on [a,b] to F(b)-F(a). That is not true of earlier attempts. That book is an MAA publication: Carus#20.