We present the rest-frame 8 m LF at redshifts z ¼ 1 and $2, computed from Spitzer 24 m-selected galaxies in the GOODS fields over an area of 291 arcmin 2 . Using classification criteria based on X-ray data and IRAC colors, we identify the AGNs in our sample. The rest-frame 8 m LFs for star-forming galaxies at redshifts z ¼ 1 and $2 have the same shape as at z $ 0, but with a strong positive luminosity evolution. The number density of star-forming galaxies with log 10 (L 8 m ) > 11 increases by a factor >250 from redshift z $ 0 to 1 and is basically the same at z ¼ 1 and $2. The resulting rest-frame 8 m luminosity densities associated with star formation at z ¼ 1 and $2 are more than 4 and 2 times larger than at z $ 0, respectively. We also compute the total rest-frame 8 m LF for star-forming galaxies and AGNs at z $ 2 and show that AGNs dominate its bright end, which is well described by a power law. Using a new calibration based on Spitzer star-forming galaxies at 0 < z < 0:6 and validated at higher redshifts through stacking analysis, we compute the bolometric IR LF for star-forming galaxies at z ¼ 1 and $2. We find that the respective bolometric IR luminosity densities are (1:2 AE 0:2) ; 10 9 and (6:6 þ1:2 À1:0 ) ; 10 8 L Mpc À3 , in agreement with previous studies within the error bars. At z $ 2, around 90% of the IR luminosity density associated with star formation is produced by luminous and ultraluminous IR galaxies, with the two populations contributing in roughly similar amounts. Finally, we discuss the consistency of our findings with other existing observational results on galaxy evolution.

Aims. We present the observed correlations between rest-frame 8, 24, 70 and 160 µm monochromatic luminosities and measured total infrared luminosities L IR of galaxies detected by Spitzer. Methods. Our sample consists of 372 star-forming galaxies with individual detections and flux measurements at 8, 24, 70 and 160 µm. We have spectroscopic redshifts for 93% of these sources, and accurate photometric redshifts for the remainder. We also used a stacking analysis to measure the IR fluxes of fainter sources at higher redshifts. Results. We show that the monochromatic mid and far-infrared luminosities are strongly correlated with the total infrared luminosity and our stacking analysis confirms that these correlations also hold at higher redshifts. We provide relations between monochromatic luminosities and total infrared luminosities L IR that should be reliable up to z ∼ 2 (z ∼ 1.1) for ULIRGs (LIRGs). In particular, we can predict L IR with accuracies of 37% and 54% from the 8 and 24 µm fluxes, while the best tracer is the 70 µm flux. Combining bands leads to slightly more accurate estimates. For example, combining the 8 and 24 µm luminosities predicts L IR with an accuracy of 34%. Our results are generally compatible with previous studies, and the small changes are probably due to differences in the sample selection criteria. We can rule out strong evolution in dust properties with redshift up to z ∼ 1. Finally, we show that infrared and sub-millimeter observations are complementary means of building complete samples of star-forming galaxies, with the former being more sensitive for z < ∼ 2 and the latter at higher z > ∼ 2.