We report on measurements of differential cross sections d sigma/d p_t for prompt charm meson production in p anti-p collisions at s**(1/2) = 1.96 TeV using 5.8 +/- 0.3 pb-1 of data from the CDF II detector at the Fermilab Tevatron. The data are collected with a new trigger that is sensitive to the long lifetime of hadrons containing heavy flavor. The charm meson cross sections are measured in the central rapidity region |y| \leq 1 in four fully reconstructed decay modes: D0 --> K- pi+, D*+ -> D0 pi+, D+ --> K- pi+ pi+, D+_s--> phi pi+, and their charge conjugates. The measured cross sections are compared to theoretical calculations.
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