The remnant of the supernova of 1006 AD, the remnant first showing evidence for the presence of X-ray synchrotron emission from shock-accelerated electrons, was observed for ~1000 ksec with INTEGRAL for the study of electron acceleration to very high energies. The aim of the observation was to characterize the synchrotron emission, and attempt to detect non-thermal bremsstrahlung, using the combination of IBIS and JEM-X spatial and spectral coverage. The source was detected with JEM-X between 2.4 and 8.4 keV bands, and not detected with either ISGRI or SPI above 20 keV. The ISGRI upper limit is about a factor of four above current model predictions, but confirms the presence of steepening in the power-law extrapolated from lower energies (< 4 keV).