  We report contributions to cosmic infrared background (CIB) intensities
originating from known galaxies and their faint companions at submillimeter
wavelengths. Using the publicly-available UltraVISTA catalog, and maps at 250,
350, and 500 {\mu}m from the \emph{Herschel} Multi-tiered Extragalactic Survey
(HerMES), we perform a novel measurement that exploits the fact that
uncatalogued sources may bias stacked flux densities --- particularly if the
resolution of the image is poor --- and intentionally smooth the images before
stacking and summing intensities. By smoothing the maps we are capturing the
contribution of faint (undetected in K_S ~ 23.4) sources that are physically
associated, or correlated, with the detected sources. We find that the
cumulative CIB increases with increased smoothing, reaching 9.82 +- 0.78, 5.77
+- 0.43, and 2.32 +- 0.19$\, \rm nW m^{-2} sr^{-1}$ at 250, 350, and 500 {\mu}m
at 300 arcsec FWHM. This corresponds to a fraction of the fiducial CIB of 0.94
+- 0.23, 1.07 +- 0.31, and 0.97 +- 0.26 at 250, 350, and 500 {\mu}m, where the
uncertainties are dominated by those of the absolute CIB. We then propose, with
a simple model combining parametric descriptions for stacked flux densities and
stellar mass functions, that emission from galaxies with log(M/Msun) > 8.5 can
account for the most of the measured total intensities, and argue against
contributions from extended, diffuse emission. Finally, we discuss prospects
for future survey instruments to improve the estimates of the absolute CIB
levels, and observe any potentially remaining emission at z > 4.
