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 } L _ { \odot } and 10 ^ { 11.8 } L _ { \odot } . We have combined new narrow-band H \alpha + [ N ii ] 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 \sim 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 \sim 1 Gyr ago with stellar masses between 10 ^ { 10.1 } and 10 ^ { 11.5 } M _ { \odot } . 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 .