We present the analysis of the integrated spectral energy distribution (SED) from the ultraviolet (UV) to the far-infrared and H$alpha$ of a sample of 29 local systems and individual galaxies with infrared (IR) luminosities between 10^11 Lsun and 10^11.8 Lsun. We have combined new narrow-band H$alpha$+[NII] and broad-band g, r optical imaging taken with the Nordic Optical Telescope (NOT), with archival GALEX, 2MASS, Spitzer, and Herschel data. The SEDs (photometry and integrated H$alpha$ flux) have been fitted with a modified version of the MAGPHYS code using stellar population synthesis models for the UV-near-IR range and thermal emission models for the IR emission taking into account the energy balance between the absorbed and re-emitted radiation. From the SED fits we derive the star-formation histories (SFH) of these galaxies. For nearly half of them the star-formation rate appears to be approximately constant during the last few Gyrs. In the other half, the current star-formation rate seems to be enhanced by a factor of 3-20 with respect to that occured ~1 Gyr ago. Objects with constant SFH tend to be more massive than starbursts and they are compatible with the expected properties of a main-sequence (M-S) galaxy. Likewise, the derived SFHs show that all our objects were M-S galaxies ~1 Gyr ago with stellar masses between 10^10.1 and 10^11.5 Msun. We also derived from our fits the average extinction (A_v=0.6-3 mag) and the polycyclic aromatic hydrocarbons (PAH) luminosity to L(IR) ratio (0.03-0.16). We combined the A_v with the total IR and H$alpha$ luminosities into a diagram which can be used to identify objects with rapidly changing (increasing or decreasing) SFR during the last 100 Myr.
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