The 0.4 < z < 1.3 star formation history of the Universe as viewed in the far-infrared

[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.