We exploit the gravitational potential of massive cluster lenses to probe the emission line properties of six z=1 galaxies which appear as highly magnified luminous arcs. Using the GMOS integral field spectrograph together with detailed cluster lens models we reconstruct the intrinsic morphologies and two-dimensional velocity fields in these galaxies on scales corresponds to \~0.5kpc (unlensed) at z=1. Four of the galaxies have stable disk-like kinematics, whilst the other two resemble interacting or starburst galaxies. These galaxies lie close to the mean rest-frame I-band Tully-Fisher relation for nearby spirals suggesting a clear preference for hierarchical growth of structure. In the rest-frame B-band, the observations suggest 0.5+/-0.3mag of brightening, consistent with increased star-formation activity at z=1. However, the galaxies with stable disk kinematics have more slowly rising rotation curves than expected from galaxies with similar surface brightness in the local Universe. We suggest that this may arise because the distant galaxies have lower bulge masses than their local counter-parts. Whilst this study is based on only six galaxies, the gain in flux and in spatial resolution achieved via gravitational magnification provides a much more detailed view of the high redshift Universe than possible with conventional surveys.