This is from the paper "The Halpha Galaxy Survey V. The star formation history of late type galaxies", by Phil James et al. astro-ph/0804.2167

They have SFRs from Halpha, stellar masses from K and R band photometry (all with the 1m Kapteyn Telescope) and gas masses from Westerbork neutral hydrogen observations for local late type field galaxies. Here they plot the star formation timescale (Mstar/SFR) and gas depletion timescale (Mgas/SFR) for galaxies as a function of mass and type. The dashed lines indicate the age of the universe. The fact that the star formation timescale for low mass/late type galaxies is similar to the age of the universe and their gas depletion time is much longer, whereas it is reversed for the high mass/earlier type galaxies is used as an argument that the star formation history of very late type galaxies is constant over the age of the universe and the stellar mass gradually builds up, an that for more bulgy galaxies the bulk of the star formation happens in short bursts of high SFR.

The possibility of having a higher SFR in the past is not mentioned...