Can you recommend some nice papers or texts that discuss in detail the different ways to define Riemann integrability (for bounded functions defined on a compact interval of the real line)?
For instance, the main approach in Spivak's book is via upper and lower sums; it is only in an appendix that he brings up Riemann sums. What would be an example of a serious book that develops the theory the other way round (Riemann sums first)?
Thanks in advance for your suggestions.