  [Abridged] We use the deepest existing mid- and far-infrared observations
(reaching ~3 mJy at 70 um) obtained with Spitzer in the GOODS and FIDEL fields
to derive the evolution of the rest-frame 15 um, 35 um, and total infrared
luminosity functions of galaxies spanning z < 1.3. In comparison with previous
studies, the present one takes advantage of deep 70 um observations that
provide a more robust infrared luminosity indicator than 24 um affected by the
emission of PAHs at high redshift (z~1), and we use several independent fields
to control cosmic variance. We use a new extraction technique based on the
well-determined positions of galaxies at shorter wavelengths to extract the 24
and 70 um flux densities of galaxies. Using a combination of photometric and
spectroscopic redshifts that exist for ~80% of the sources in our sample, we
are able to estimate the rest-frame luminosities of galaxies at 15um and 35um.
Then using a careful stacking analysis to validate the infrared bolometric
corrections we compute the infrared luminosity function in three redshift bins
z~0.55, z~0.85, and z~1.15. We find that the average infrared spectral energy
distribution of galaxies over the last 2/3 of the cosmic time is consistent
with that of local galaxies, although individual sources do present significant
scatter. We also measured both the bright and faint ends of the infrared
luminosity functions and find no evidence for a change in the slope of the
double power law used to characterize the luminosity function. The redshift
evolution of infrared luminous galaxies is consistent with pure luminosity
evolution proportional to (1+z)^3.6 up to z~1.3. The comoving number density of
infrared luminous galaxies has increased by a factor of ~100 between 0< z <1.
By z~1.0, LIRGs produce half of the total comoving infrared luminosity density.
