[en] We present a determination of the Cabibbo-Kobayashi-Maskawa matrix elements vertical stroke V_cd vertical stroke and vertical stroke V_cs vertical stroke obtained by combining the momentum dependence of the semileptonic vector form factors f₊^D→π(q²) and f₊^D→K(q²), recently determined from lattice QCD simulations, with the differential rates measured for the semileptonic D → πlν and D → Klν decays. Our analysis is based on the results for the semileptonic form factors produced by the European Twisted Mass Collaboration with N_f = 2 + 1 + 1 flavors of dynamical quarks in the whole range of values of the squared 4-momentum transfer accessible in the experiments. The statistical and systematic correlations between the lattice data as well as those present in the experimental data are properly taken into account. With respect to the standard procedure based on the use of only the vector form factor at zero 4-momentum transfer, we obtain more precise and consistent results: vertical stroke V_cd vertical stroke = 0.2341 (74) and vertical stroke V_cs vertical stroke = 0.970 (33). The second-row CKM unitarity is fulfilled within the current uncertainties: vertical stroke V_cd vertical stroke ² + vertical stroke V_cs vertical stroke ² + vertical stroke V_cb vertical stroke ² = 0.996 (64). Moreover, using for the first time hadronic inputs determined from first principles, we have calculated the ratio of the semileptonic D → π(K) decay rates into muons and electrons, which represent a test of lepton universality within the SM, obtaining in the isospin-symmetric limit of QCD: R_LU^Dπ = 0.985 (2) and R_LU^DK = 0.975 (1). (orig.)