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We present new observational determination of the evolution of the rest-frame 70 and 160µm and total infrared (TIR) galaxy luminosity functions (LFs) using 70 and 160µm data from the Spitzer Wide-area Infrared Extragalactic (SWIRE) Legacy survey. The LFs were constructed for sources with spectroscopic redshifts only in the XMM-LSS and Lockman Hole fields from the SWIRE photometric redshift catalogue. The 70µm and TIR LFs were constructed in the redshift range 0 < z < 1.2 and the 160µm LF was constructed in the redshift range 0 < z < 0.5 using a parametric Bayesian and the 1/Vmax methods. We assume in our models that the faint-end power-law index of the LF does not evolve with redshift. We find that the double power-law model is a better representation of the infrared (IR) LF than the more commonly used power-law and Gaussian model. We model the evolution of the far-IR LFs as a function of redshift where the characteristic luminosity L* evolve as ∝(1+z)^α_L. The rest-frame 70µm LF shows a strong luminosity evolution out to z = 1.2 with α_L=3.41^+0.18_-0.25. The rest-frame 160µm LF also showed rapid luminosity evolution with α_L=5.53^+0.28_-0.23 out to z = 0.5. The rate of evolution in luminosity is consistent with values estimated from previous studies using data from IRAS, ISO and Spitzer. The TIR LF evolves in luminosity with α_L=3.82^+0.28_-0.16 which is in agreement with previous results from Spitzer 24µm which find strong luminosity evolution. By integrating the LF we calculated the comoving IR luminosity density out to z = 1.2, which confirms the rapid evolution in number density of luminous IR galaxies which contribute ∼ 68+ 10- 07 per cent to the comoving star formation rate density at z = 1.2. Our results based on 70µm data confirm that the bulk of the star formation at z = 1 takes place in dust-obscured objects.