We estimate the contribution of AGNs and of their host galaxies to the infrared background. We use the luminosity function and evolution of AGNs recently determined by the hard X-ray surveys, and new Spectral Energy Distributions connecting the X-ray and the infrared emission, divided in intervals of absorption. These two ingredients allow us to determine the contribution of AGNs to the infrared background by using mostly observed quantities, with only minor assumptions. We obtain that AGN emission contributes little to the infrared background ($<$5% over most of the infrared bands), implying that the latter is dominated by star formation. However, AGN host galaxies may contribute significantly to the infrared background, and more specifically 10--20% in the 1--20$mu$m range and $sim$5% at $lambda<60mu m$. We also give the contribution of AGNs and of their host galaxies to the source number counts in various infrared bands, focusing on those which will be observed with Spitzer. We also report a significant discrepancy between the expected contribution of AGN hosts to the submm background and bright submm number counts with the observational constraints. We discuss the causes and implications of this discrepancy and the possible effects on the Spitzer far-IR bands.
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