  We present deep number counts at 450 and 850 $\mu$m using the SCUBA-2 camera
on the James Clerk Maxwell Telescope. We combine data for six lensing cluster
fields and three blank fields to measure the counts over a wide flux range at
each wavelength. Thanks to the lensing magnification, our measurements extend
to fluxes fainter than 1 mJy and 0.2 mJy at 450 $\mu$m and 850 $\mu$m,
respectively. Our combined data highly constrain the faint end of the number
counts. Integrating our counts shows that the majority of the extragalactic
background light (EBL) at each wavelength is contributed by faint sources with
$L_{\rm IR} < 10^{12} L_{\odot }$, corresponding to luminous infrared galaxies
(LIRGs) or normal galaxies. By comparing our result with the 500 $\mu$m
stacking of $K$-selected sources from the literature, we conclude that the
$K$-selected LIRGs and normal galaxies still cannot fully account for the EBL
that originates from sources with $L_{\rm IR} < 10^{12} L_{\odot }$. This
suggests that many faint submillimeter galaxies may not be included in the UV
star formation history. We also explore the submillimeter flux ratio between
the two bands for our 450 $\mu$m and 850 $\mu$m selected sources. At 850
$\mu$m, we find a clear relation between the flux ratio and the observed flux.
This relation can be explained by a redshift evolution, where galaxies at
higher redshifts have higher luminosities and star formation rates. In
contrast, at 450 $\mu$m, we do not see a clear relation between the flux ratio
and the observed flux.

Astrophysics of Galaxies