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 \sim 150 keV with a very hard power-law spectrum with photon index \Gamma = 0.73 \pm 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 \sim 75 keV and \sim 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 \pm 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 .