The T2K (Tokai-to-Kamioka) experiment is a long baseline neutrino oscillation experiment built, primarily, to measure the neutrino mixing angle 13. To determine this parameter with minimal uncertainty requires a good understanding of the initial neutrino flux in the beam and precise measurements of neutrino interactions with matter. For this reason, T2K employs a near detector placed 280m downstream of the neutrino production point, the ND280. Using data taken by the ND280 between November 2010 and April 2013 (5:73x1020 protons on target), a flux-integrated muon antineutrino charged-current inclusive cross-section measurement per nucleon using the carbon target of the ND280 FGD1 is reported, including a description of the event selection and the systematic uncertainty evaluation. The final result is: [Result unable to be displayed] at a mean muon antineutrino energy of 1 GeV. The uncertainty on this measurement is dominated by neutrino flux uncertainties. A possible method of improving the precision with which the flux is known is presented, which indicates that at the end of the expected T2K data-taking period, this uncertainty can be reduced from 12:4% to 5:8%.