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We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from the connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical u, d, s, and c quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from a≈0.06 to 0.15 fm. The up- and down-quark masses in our simulations have equal masses ml. We obtain, in this world where all pions have the mass of the π0, 1010aμll(conn.)=637.8(8.8), in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total O(α2) hadronic-vacuum polarization to the muon's anomalous magnetic moment is 1010aμHVP,LO=699(15)u,d(1)s,c,b, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both ab-initio lattice-QCD calculations and phenomenological determinations from experimental e+e−-scattering data. It is 1.3σ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of aμ with theoretical calculations of the other contributions.