accepted for publication in A&A, 13 pages, 9 figures (3 in colour)The INTEGRAL satellite extensively observed the black hole binary Cygnus X-1 from 2002 November to 2004 November during calibration, open time and core program (Galactic Plane Scan) observations. These data provide evidence for significant spectral variations over the period. In the framework of the accreting black hole phenomenology, the source was most of the time in the Hard State and occasionally switched to the so-called "Intermediate State". Using the results of the analysis performed on these data, we present and compare the spectral properties of the source over the whole energy range (5 keV - 1 MeV) covered by the high-energy instruments on board INTEGRAL, in both ob...