  A simple and versatile parameterized approach to the star formation history
allows a quantitative investigation of the constraints from far infrared and
submillimetre counts and background intensity measurements.
  The models include four spectral components: infrared cirrus (emission from
interstellar dust), an M82-like starburst, an Arp220-like starburst and an AGN
dust torus. The 60 $\mu$m luminosity function is determined for each chosen
rate of evolution using the PSCz redshift data for 15000 galaxies. The
proportions of each spectral type as a function of 60 $\mu$m luminosity are
chosen for consistency with IRAS and SCUBA colour-luminosity relations, and
with the fraction of AGN as a function of luminosity found in 12 $\mu$m
samples. The luminosity function for each component at any wavelength can then
be calculated from the assumed spectral energy distributions. With assumptions
about the optical seds corresponding to each component and, for the AGN
component, the optical and near infrared counts can be accurately modelled.
  A good fit to the observed counts at 0.44, 2.2, 15, 60, 90, 175 and 850
$\mu$m can be found with pure luminosity evolution in all 3 cosmological models
investigated: $\Omega_o$ = 1, $\Omega_o$ = 0.3 ($\Lambda$ = 0), and $\Omega_o$
= 0.3, $\Lambda$ = 0.7.
  All 3 models also give an acceptable fit to the integrated background
spectrum. Selected predictions of the models, for example redshift
distributions for each component at selected wavelengths and fluxes, are shown.
  The total mass-density of stars generated is consistent with that observed,
in all 3 cosmological models.
