We derive a variety of physical parameters including star formation rates (SFRs), dust attenuation and burst mass fractions for 6472 galaxies observed by the Galaxy Evolution Explorer (GALEX) and present in the SDSS DR1 main spectroscopic sample. Parameters are estimated in a statistical way by comparing each observed broad-band SED (two GALEX and five SDSS bands) with an extensive library of model galaxy SEDs, which cover a wide range of star formation histories and include stochastic starbursts. We compare the constraints derived using SDSS bands only with those derived using the combination of SDSS and GALEX photometry. We find that the addition of the GALEX bands leads to significant improvement in the estimation of both the dust optical depth and the star formation rate over timescales of 100 Myr to 1 Gyr in a galaxy. We are sensitive to SFRs as low as 10^{-3} M_sun/yr, and we find that low levels of star formation (SF) are mostly associated with early-type, red galaxies. The least massive galaxies have ratios of current to past-averaged SF rates (b-parameter) consistent with constant SF over a Hubble time. For late-type galaxies, this ratio on average decreases with mass. We find that b correlates tightly with NUV-r color, implying that the SF history of a galaxy can be constrained on the basis of the NUV-r color alone. The fraction of galaxies that have undergone a significant starburst episode within the last 1 Gyr steeply declines with mass-from ~20% for galaxies with ~10^8 M_sun to ~5% for ~10^11 M_sun galaxies.
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