  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.
