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We use new deep near-infrared (NIR) and mid-infrared (MIR) observations toanalyze the 850$~\mu$m image of the GOODS HDF-N region. We show that much ofthe submillimeter background at this wavelength is picked out by sources with$H(AB)$ or 3.6um (AB)<23.25 (1.8 uJy). These sources contribute an 850umbackground of 24\pm2 Jy deg^-2. This is a much higher fraction of the measuredbackground (31-45 Jy deg^-2) than is found with current 20cm or 24um samples.Roughly one-half of these NIR-selected sources have spectroscopicidentifications, and we can assign robust photometric redshifts to nearly allof the remaining sources using their UV to MIR spectral energy distributions.We use the redshift and spectral type information to show that a large fractionof the 850um background light comes from sources with z=0-1.5 and that thesources responsible have intermediate spectral types. Neither the ellipticalgalaxies, which have no star formation, nor the bluest galaxies, which havelittle dust, contribute a significant amount of 850um light, despite the factthat together they comprise approximately half of the galaxies in the sample.The galaxies with intermediate spectral types have a mean flux of 0.40\pm0.03mJy at 850um and 9.1\pm0.3 uJy at 20cm.  The redshift distribution of the NIR-selected 850um light lies well belowthat of the much smaller amount of light traced by the more luminous, radio-selected submillimeter sources. We therefore require a revised star-formationhistory with a lower star-formation rate at high redshifts. We use a stackinganalysis of the 20cm light in the NIR sample to show that the star-formationhistory of the total 850um sample is relatively flat down to z~1 and that halfof the total star formation occurs at redshifts z<1.4.Comment: 14 pages, 15 figures. Accepted by The Astrophysical Journal for v647n  1 issue, August 2006. Minor changes in response to the referee's report, plus  a new comparison figure of the star formation history measured in the FIR  with that measured in the UV. We plot d(rho)/dt x cosmic time vs. cosmic  time, which has the advantage of illustrating more directly how many stars  are formed at a given tim

A Near‐Infrared Analysis of the Submillimeter Background and the Cosmic Star‐Formation History