We report a measurement of the flux-integrated cross section for inclusive muon neutrino charged-current interactions on carbon. The double differential measurements are given as function of the muon momentum and angle. Relative to our previous publication on this topic, these results have an increased angular acceptance and higher statistics. The data sample presented here corresponds to $5.7 times 10^{20}$ protons-on-target. The total flux-integrated cross section is measured to be $(6.950 pm 0.662) times 10^{-39}$ cm$^2$nucleon$^{-1}$ and is consistent with our simulation.