Using 281 /pb of e^+ e^- collisions recorded at the psi(3770) resonance with the CLEO-c detector at CESR, we determine absolute hadronic branching fractions of charged and neutral D mesons using a double tag technique. Among measurements for three D^0 and six D^+ modes, we obtain reference branching fractions B(D^0 --> K^-pi^+) = (3.891 +- 0.035 +- 0.059 +- 0.035)% and B(D^+ --> K^-pi^+pi^+) = (9.14 +- 0.10 +- 0.16 +- 0.07)%, where the first uncertainty is statistical, the second is all systematic errors other than final state radiation (FSR), and the third is the systematic uncertainty due to FSR. We include FSR in these branching fractions by allowing for additional unobserved photons in the final state. Using an independent determination of the integrated luminosity, we also extract the cross sections sigma(e+e- --> D^0 D^0-bar) = (3.66+- 0.03 +- 0.06) nb and sigma(e+e- --> D^+ D^-) = (2.91+- 0.03 +- 0.05) nb at a center of mass energy, E_cm = 3774 +- 1 MeV.
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