We present a new study of the form factors for D -> K semileptonic decay from lattice QCD that allows us to compare the shape of the vector form factor to experiment and, for the first time, to extract V_cs using results from all experimental q^2 bins. The valence quarks are implemented with the Highly Improved Staggered Quark action on MILC configurations that include u, d and s sea quarks. The scalar and vector currents are nonperturbatively normalised and, using phased boundary conditions, we are able to cover the full q^2 range accessible to experiment. Our result is V_cs = 0.963(5)_{expt}(14)_{lattice}. We also demonstrate that the form factors are insensitive to whether the spectator quark is u/d or s, which has implications for other decay channels.
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