The star formation rate (SFR) is one of the main parameters used to analyze the evolution of galaxies through time. The need for recovering the light reprocessed by dust commonly requires the use of low spatial resolution far-infrared data. Recombination line luminosities provide an alternative, although uncertain dust-extinction corrections based on narrowband imaging or long-slit spectroscopy have traditionally posed a limit to their applicability. Integral field spectroscopy (IFS) is clearly the way to overcome this kind of limitation. Aims. We obtain integrated Hα, ultraviolet (UV) and infrared (IR)-based SFR measurements for 272 galaxies from the CALIFA survey at 0.005 <z< 0.03 using single-band and hybrid tracers. We aim to determine whether the extinction-corrected Hα luminosities provide a good measure of the SFR and to shed light on the origin of the discrepancies between tracers. Updated calibrations referred to Hα are provided. The well-defined selection criteria and large statistics allow us to carry out this analysis globally and split by properties, including stellar mass and morphological type. Methods. We derive integrated, extinction-corrected Hα fluxes from CALIFA, UV surface and asymptotic photometry from GALEX and integrated WISE 22 μm and IRAS fluxes. Results. We find that the extinction-corrected Hα luminosity agrees with the hybrid updated SFR estimators based on either UV or Hα plus IR luminosity over the full range of SFRs (0.03-20 M⊙ yr-1). The coefficient that weights the amount of energy produced by newly-born stars that is reprocessed by dust on the hybrid tracers, aIR, shows a large dispersion. However, this coefficient does not became increasingly small at high attenuations, as expected if significant highly-obscured Hα emission were missed, i.e., after a Balmer decrement-based attenuation correction is applied. Lenticulars, early-type spirals, and type-2 AGN host galaxies show smaller coefficients because of the contribution of optical photons and AGN to dust heating. Conclusions. In the local Universe, the Hα luminosity derived from IFS observations can be used to measure SFR, at least in statistically-significant, optically-selected galaxy samples, once stellar continuum absorption and dust attenuation effects are accounted for. The analysis of the SFR calibrations by galaxies properties could potentially be used by other works to study the impact of different selection criteria in the SFR values derived, and to disentangle selection effects from other physically motivated differences, such as environmental or evolutionary effects.