  Multiwavelength observations are essential to constrain physical parameters
of the blazars observed by Fermi/LAT. Among the 187 AGN significantly detected
in public INTEGRAL data above 20 keV by the imager IBIS/ISGRI, 20 blazars were
detected. 15 of these sources allowed significant spectral extraction. They
show hard X-ray spectra with an average photon index of 2.1+-0.1 and a hard
X-ray luminosity of L(20-100 keV) = 1.3e46 erg/s. 15 of the INTEGRAL blazars
are also visible in the first 16 months of the Fermi/LAT data, thus allowing to
constrain the inverse Compton branch in these cases. Among others, we analyse
the LAT data of four blazars which were not included in the Fermi LAT Bright
AGN Sample based on the first 3 months of the mission: QSO B0836+710, H
1426+428, RX J1924.8-2914, and PKS 2149-306. Especially for blazars during
bright outbursts, as already observed simultaneously by INTEGRAL and Fermi
(e.g. 3C 454.3 and Mrk 421), INTEGRAL provides unique spectral coverage up to
several hundred keV. We present the spectral analysis of INTEGRAL and Fermi
data and demonstrate the potential of INTEGRAL observations of Fermi detected
blazars in outburst by analysing the combined data set of the persistent radio
galaxy Cen A.
