  We investigate the redshift dependence of the contribution to the
extragalactic far-infrared/sub-millimeter background from galaxies detected by
the Spitzer Space Telescope at 8um and 24um. Using seven-band optical to
mid-infrared photometry, we estimate photometric redshifts for the Spitzer
sources which appear to be mostly L* galaxies at a median redshift of z=1.0.
These sources, extracted from deep 8um and 24um mosaics of the CUDSS 14-hour
field with 5sigma limits of 5.8uJy and 70uJy respectively, exhibit significant
850um and 450um emission as observed by SCUBA. At 850um, after removing
>=4sigma sources and those securely identified in our previous cross-matching
paper, we measure stacked flux at the significance level of 4.4sigma and
2.9sigma from the full 8um and 24um galaxy catalogue respectively. At 450um,
flux is detected from all 8um galaxies at the level of 3.5sigma, while there is
no significant emission from the 24um galaxies. We find that the 850um flux is
emitted almost exclusively at z>~1.3 from the Spitzer sources with 0.44mJy
(4.7sigma) per 8um source and 0.51mJy (2.8sigma) per 24um source. This
corresponds to a contribution of (16+/-3)% toward the 850um extra-galactic
background from the 8um sources and (5.0+/-1.8)% from the 24um sources. At
450um, only the 8um sources within the redshift interval 1<z<2 exhibit
significant emission with an average flux per source of 3.35mJy (3.0sigma).
This is a contribution of (37+/-12)% to the 450um background.
