In this paper, we present INTEGRAL observations of seven active galactic nuclei (AGNs): two newly discovered type 1 Seyferts, IGR J18027−1455 and J21247+5058 and five well‐known Seyferts, NGC 6814 (type 1.5), Cygnus A (type 2), MCG‐05‐23‐16 (type 2), ESO 103‐G035 (type 2) and GRS 1734‐292. For IGR J18027−1455 and J21247+5058, only INTEGRAL/IBIS data were available, while broad‐band spectra are presented and discussed for the remaining five sources for which either BeppoSAX or ASCA data were used in conjunction with INTEGRAL measurements. In the cases of NGC 6814 and GRS 1734‐292, data taken in different periods indicate variability in the flux: in the case of NGC 6814 by a factor of 16 over a period of about 10 years. Although limited in size, our sample can be used to investigate the parameter space of both the photon index and cut‐off energy. The mean photon index is 1.8, while the cut‐off energy ranges from 30–50 keV to greater than 200 keV; in the particular case of MCG‐05‐23‐16, ESO 103‐G035 and GRS 1734‐292, the cut‐off energy is well constrained at or below 100 keV. We have also tested an enlarged sample, which includes INTEGRAL data of three more AGNs, against the correlation found by a number of authors between the photon index and the cut‐off energy but have found no evidence for a relation between these two parameters. Our analysis indicates that there is a diversity in cut‐off energies in the primary continuum of Seyfert galaxies.