  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, 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.
  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. The total mass-density of stars generated is
consistent with that observed, in all 3 cosmological models.
