The invariant differential cross section for inclusive electron production in p+p collisions at [FORMULA: SEE TEXT] has been measured by the PHENIX experiment at the BNL Relativistic Heavy Ion Collider over the transverse momentum range 0.4<or=pT<OR=5.0 GeV/c in the central rapidity region ([FORMULA: SEE TEXT]). The contribution to the inclusive electron spectrum from semileptonic decays of hadrons carrying heavy flavor, i.e., charm quarks or, at high , bottom quarks, is determined via three independent methods. The resulting electron spectrum from heavy-flavor decays is compared to recent leading and next-to-leading order perturbative QCD calculations. The total cross section of charm quark-antiquark pair production is determined to be [FORMULA: SEE TEXT].