What are necessary and sufficient conditions in order that a function may be an indefinite integral in the Riemann sense? The problem has been explicitly posed in a short note  published by Erik Talvila in 2008 in THIS EXCHANGE. Since neither Erik nor I have been able to find a solution in the literature I propose the following solution which is the sole subject of the paper.
"Characterizations of an Indefinite Riemann Integral." Real Anal. Exchange 35 (2) 487 - 492, 2009/2010.