We obtained SMA observations of eight faint (intrinsic 850 $mu$m fluxes $<$ 2 mJy) submillimeter galaxies (SMGs) discovered in SCUBA images of the massive lensing cluster fields A370, A2390, and A1689 and detected five. In total, we obtain 5 SMA detections, all of which have de-lensed fluxes $<$1 mJy with estimated total infrared luminosities 10$^{10}-10^{12}$ $L_odot$, comparable to luminous infrared galaxies (LIRGs) and normal star-forming galaxies. Based on the latest number counts, these galaxies contribute $sim$70% of the 850 $mu$m extragalactic background light and represent the dominant star-forming galaxy population in the dusty universe. However, only 40$^{+30}_{-16}$% of our faint SMGs would be detected in deep optical or near-infrared surveys, which suggests many of these sources are at high redshifts ($z gtrsim 3$) or extremely dusty, and they are not included in current star formation history estimates.
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