We have performed observations of the blazar S5 0716+714 with INTEGRAL on 2-6 April 2004. In the first months of 2004, the source had increased steadily in optical brightness and had undergone two outbursts. During the latter outburst, that occurred in March, it reached the extreme level of R = 12.1 mag, which triggered our INTEGRAL program. The target has been detected with IBIS/ISGRI up to 60 keV, with a flux of ∼3 × 10 −11 erg s −1 cm −2 in the 30-60 keV interval, a factor of ∼2 higher than observed by the BeppoSAX PDS in October 2000. In the field of S5 0716+714 we have also detected the Flat Spectrum Radio Quasar S5 0836+710 and the two Seyfert galaxies Mkn 3 and Mkn 6. Their IBIS/ISGRI spectra are rather flat, albeit consistent with those measured by BeppoSAX. In the spectrum of Mkn 3 we find some evidence of a break between ∼60 and ∼100 keV, reminiscent of the high energy cut-offs observed in other Seyfert galaxies. This is the first report of INTEGRAL spectra of weak Active Galactic Nuclei.