The COBE FIRAS data contain foreground emission from interplanetary, Galact
ic interstellar dust and extragalactic background emission. We use three di
fferent methods to separate the Various emission components, and derive the
spectrum of the extragalactic far-infrared background (FIRB). Each method
relies on a different set of assumptions, which affect the FIRE spectrum in
different ways. Despite this, the FIRE spectra derived by these different
methods are remarkably similar. The average spectrum that we derive in the
v = 5-80 cm(-1) (2000-125 mu m) frequency interval is I(v) = (1.3 +/- 0.4)
x 10(-5)(v/v(o))P-0.64+/-0.12(v)(18.5 +/- 1.2 K), where v(o) = 100 cm(-1) (
lambda(o) = 100 mu m), and P is the Planck function. The derived FIRE spect
rum is consistent with the (DIRBE) 140 and 240 mu m detections. The total i
ntensity received in the 5-80 cm(-1) frequency interval is 14 nW m(-2) sr(-
1) and comprises about 20% of the total intensity expected from the energy
release from nucleosynthesis throughout the history of the universe.