I present INTEGRAL observations of the prototypical sources Cygnus X-1 and GX 339-4 in various X-ray spectral states (including during the TeV detection of Cygnus X-1 by MAGIC). Detailed spectral analysis of the evolution of these sources during state transitions allows us to follow the spectral evolution from the Low Hard State (LHS: dominated by thermal comptonisation) to the High Soft State (HSS: dominated by the accretion disc thermal emission and non-thermal comptonisation in the corona). Across the transition, the accretion disc luminosity increases by at least one order of magnitude while the comptonised coronal luminosity does not changes dramatically. We also attempt to model the observed spectra using a new Fokker-Planck code accounting for the so-called ’synchrotron boiler effect’. These numerical simulations indicate that in both spectral states the magnetised corona could be powered essentially through acceleration of non-thermal particles. The main differences between the LHS and HSS coronal emission can then be understood as the consequence of the strong cooling soft photon flux from the disc present in the HSS and absent in the LHS. This suggests that, contrary to current beliefs, the corona of the HSS and that of the LHS could be of very similar nature.