  Telescopes like Herschel and the Atacama Large Millimeter/submillimeter Array
(ALMA) are creating new opportunities to study sources in the far infrared
(FIR), a wavelength region dominated by cold dust emission. Probing cold dust
in active galaxies allows for study of the star formation history of active
galactic nuclei (AGN) hosts. The FIR is also an important spectral region for
observing AGN which are heavily enshrouded by dust, such as Compton thick AGN.
By using information from deep X-ray surveys and cosmic X-ray background
synthesis models, we compute Cloudy photoionization simulations which are used
to predict the spectral energy distribution (SED) of AGN in the FIR. Expected
differential number counts of AGN and their host galaxies are calculated in the
Herschel bands. The expected contribution of AGN and their hosts to the cosmic
infrared background (CIRB) and the infrared luminosity density are also
computed. Multiple star formation scenarios are investigated using a modified
blackbody star formation SED. It is found that FIR observations at ~500 um are
an excellent tool in determining the star formation history of AGN hosts.
Additionally, the AGN contribution to the CIRB can be used to determine whether
star formation in AGN hosts evolves differently than in normal galaxies. The
contribution of Compton thick AGN to the bright end differential number counts
and to the bright source infrared luminosity density is a good test of AGN
evolution models where quasars are triggered by major mergers.
