[en] We obtain the cross sections for the reactions, ν_e+¹³C→e^-+X and ν_μ+³C→μ^-+X. For the former reaction we do this for incident neutrino energies from threshold to 100 MeV and for the latter reaction from threshold to 300 MeV. We obtain our results via a tensor model which makes use of data for the total muon capture rate in ¹³C. We also obtain the electron neutrino cross section averaged over the Michel spectrum and the muon neutrino reaction averaged over the LAMPF muon neutrino spectrum. We find that these cross sections will contribute only a few percent to the uncertainties in the ¹²C neutrino cross sections and we discuss this point in detail