  We present a detailed interpretation of the spectrum of the cosmic infrared
background longwards of 5 microns and of galaxy counts from various surveys at
mid-infrared, far-infrared and submillimeter wavelengths by evolving the
mid-infrared local luminosity function with redshift. We find that all
evolutionary models that fit the counts require a flattening at z~0.8 to avoid
overproducing the CIRB. About 80% of the 140 micron CIRB is produced at 0 < z <
1.5 while only about 30% of the 850 micron background is produced within the
same redshift range. The nature of the evolution is translated into a measure
of the dust enshrouded star formation rate density as a function of redshift
and compared with estimates from optical/near-infrared surveys. We find that
the dust obscured star formation rate density appears to peak at z=0.8+/-0.1,
much sooner than previously thought, with a value of 0.25+/-0.12 M_sun/yr and
remains almost constant up to z~2. At least 70% of this star formation takes
place in luminous infrared galaxies with L_IR > 10^11 L_sun. The long
wavelength observations that constrain our evolutionary models do not strongly
trace the evolution at z > 2 and a drop off in the dust enshrouded star
formation rate is consistent with both the CIRB spectrum and the number counts.
However, a comparison with the infrared luminosity function derived from
extinction corrected optical/UV observations of the Lyman-break galaxy (LBG)
population at z~3 suggests that the flat comoving star formation rate seen
between redshifts 0.8 and 2, extends up to a redshift of z~4.
