A notion of primitive that fits the Riemann integral

We present a notion of primitive which corresponds exactly with the Riemann integral. We obtain a characterization of the integrability in the sense of Riemann which produces a Fundamental Theorem of Calculus without special assumptions. We prove a lemma which generalizes the theorem on functions with zero derivative in an interval. We apply these concepts, sketching a simplified alternative presentation of the Riemann integral in R.