  We present a study of the submillimeter (submm) emission of Distant Red
Galaxies (DRGs). The DRGs are selected by the criterion (J-K)>2.3, and are
generally massive galaxies at redshifts higher than 2, with red rest-frame
optical colors. Using a deep SCUBA submm image of a field centred on the
cluster MS1054-03, we obtain a statistical detection of the DRGs at redshift
z=2-3.5, with an average 850um flux density of 1.11+-0.28mJy. The detection
implies an average star formation rate (SFR) of 127+-34 M_sun/yr (lensing
corrected), assuming that the far-infrared (FIR) spectral energy distribution
(SED) is well-described by a modified blackbody. The SFR derived from the submm
agrees well with SFRs derived from SED fitting of optical-near-infrared data
and average X-ray emission. Constant Star Formation models imply ages of 2Gyr,
extinction A_V=2.4 mag, which is consistent with the FIR to rest-frame optical
luminosity ratio of ~15. DRGs are older and have lower SFRs relative to optical
luminosity than (ultra-)luminous infrared galaxies, although their FIR
luminosities are similar. The DRGs at 2<z<3.5 and the Extremely Red Objects
((I-K)>4) at 1<z<2, which were also investigated, contribute 5.7 and 5.9 Jy
deg^-2 respectively to the submm background. Simple estimates suggest that
these populations contribute ~50% of the flux from sources with 0.5 < f_850 < 5
mJy, which is where the peak of energy is produced. We have therefore uncovered
one of the most important populations of galaxies contributing to the sub-mm
background.
