We have compiled a complete extragalactic sample based on 25,000 deg^2 to a limiting flux of 3E-11 ergs/cm**2/sec (7,000 deg^2 to a flux limit of 1E-11 ergs/cm**2/sec) in the 20 - 40 keV band with INTEGRAL. We have constructed a detailed exposure map to compensate for effects of non-uniform exposure. The flux-number relation is best described by a power-law with a slope of alpha = 1.66+-0.11. The integration of the cumulative flux per unit area leads to f = 2.6E-10 ergs/cm**2/sec/sr, which is about 1% of the known 20 - 40 keV X-ray background. We present the first luminosity function of AGNs in the 20-40 keV energy range, based on 38 extragalactic objects detected by the imager IBIS/ISGRI on-board INTEGRAL. The luminosity function shows a smoothly connected two power-law form, with an index of gamma_1 = 0.8 below, and gamma_2 = 2.1 above the turn-over luminosity of L* = 2.4E43 ergs/sec. The emissivity of all INTEGRAL AGNs per unit volume is W(> 1E41 ergs/sec) = 2.8E38 ergs/sec/Mpc**3. These results are consistent with those derived in the 2 - 20 keV energy band and do not show a significant contribution by Compton-thick objects. Because the sample used in this study is truly local (average z = 0.022), only limited conclusions can be drawn for the evolution of AGNs in this energy band.
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