Using the 330hr ESO-MPG 870-micron survey of the Extended Chandra Deep Field South (ECDF-S) obtained with the Large Apex BOlometer CAmera (LABOCA) on the Atacama Pathfinder EXperiment (APEX), we have carried out a stacking analysis at submillimeter (submm) wavelengths of a sample of 8266 near-infra-red (near-IR) selected (K_vega <= 20) galaxies, including 893 BzK galaxies, 1253 extremely red objects (EROs) and 737 distant red galaxies (DRGs), selected from the Multi-wavelength Survey by Yale-Chile (MUSYC). We measure average 870-micron fluxes of 0.20+-0.01mJy (20.0sigma), 0.45+-0.04mJy (11.3sigma), 0.42+-0.03mJy (14.0sigma), and 0.41+-0.04mJy (10.3sigma) for the K_vega <= 20, BzK, ERO and DRG samples, respectively. For the BzK, ERO and DRG subsamples, which overlap to some degree and are like to be at z ~ 1-2, this implies an average far-IR luminosity of ~2-6x10^{11} Lsolar and star formation rate of ~40-100Msolar. Splitting the BzK galaxies up into star-forming (sBzK) and passive (pBzK) galaxies, the former is significantly detected (0.48+-0.04mJy, 12.0sigma) while the latter is only marginally detected (0.27+-0.10mJy, 2.7sigma), thus confirming that the sBzK/pBzK criteria do isolate obscured, star forming and truly passive galaxies. The K_vega <= 20 galaxies are found to contribute with 6.6+-0.3Jy deg^{-2} (~15%) to the 870-micron extragalactic background light (EBL). sBzK and pBzK galaxies contribute 1.7+-0.2Jy deg^{-2} (~4%) and 0.2+-0.1 Jy deg^{-2} (< 0.5%) to the EBL. [Abridged]
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