We report on the results of a deep 1.6 Ms INTEGRAL observation of the Cassiopeia region performed from December 2003 to February 2004. Eleven sources were detected with the imager IBIS-ISGRI at energies above 20 keV, including three new hard X-ray sources. Most remarkable is the discovery of hard X-ray emission from the anomalous X-ray pulsar 4U 0142+61, which shows emission up to ~150 keV with a very hard power-law spectrum with photon index Gamma = 0.73 +/- 0.17. We derived flux upper limits for energies between 0.75 MeV and 30 MeV using archival data from the Compton telescope COMPTEL. In order to reconcile the very hard spectrum of 4U 0142+61 measured by INTEGRAL with the COMPTEL upper limits, the spectrum has to bend or break between ~75 keV and ~750 keV. 1E 2259+586, another anomalous X-ray pulsar in this region, was not detected. INTEGRAL and COMPTEL upper limits are provided. The new INTEGRAL sources are IGR J00370+6122 and IGR J00234+6144. IGR J00370+6122 is a new supergiant X-ray binary with an orbital period of 15.665 +/- 0.006 days, derived from RXTE All-Sky Monitor data. Archival BeppoSAX Wide-Field Camera data yielded four more detections. IGR J00234+6144 still requires a proper identification. Other sources for which INTEGRAL results are presented are high-mass X-ray binaries 2S 0114+650, Gamma~Cas, RX J0146.9+6121 and 4U 2206+54, intermediate polar V709 Cas and 1ES 0033+595, an AGN of the BL-Lac type. For each of these sources the hard X-ray spectra are fitted with different models and compared with earlier published results.
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