  Infrared (IR) luminosity is fundamental to understanding the cosmic star
formation history and AGN evolution. The AKARI IR space telescope performed all
sky survey in 6 IR bands (9, 18, 65, 90, 140, and 160um) with 3-10 times better
sensitivity than IRAS, covering the crucial far-IR wavelengths across the peak
of the dust emission. Combined with a better spatial resolution, AKARI can much
more precisely measure the total infrared luminosity (L_TIR) of individual
galaxies, and thus, the total infrared luminosity density in the local
Universe. By fitting IR SED models, we have re-measured L_TIR of the IRAS
Revised Bright Galaxy Sample. We present mid-IR monochromatic luminosity to
L_TIR conversions for Spitzer 8,24um, AKARI 9,18um, IRAS 12um, WISE 12,22um,
and ISO 15um filters, with scatter ranging 13-44%. The resulting AKARI IR
luminosity function (LF) agrees well with that from the IRAS. We integrate the
LF weighted by L_TIR to obtain a cosmic IR luminosity density of Omega_TIR=
(8.5^{+1.5}_{-2.3})x 10^7 L Mpc^-3, of which 7+-1% is produced by LIRGs, and
only 0.4+-0.1% is from ULIRGs in the local Universe. Once IR contributions from
AGN and star-forming galaxies (SFG) are separated, SFG IR LF shows a steep
decline at the bright-end. Compared with high-redshift results from the AKARI
NEP deep survey, these data show a strong evolution of Omega_TIRSF propto
(1+z)^4.0+-0.5, and Omega_TIRAGN propto (1+z)^4.4+-0.4. For Omega_TIRAGN, the
ULIRG contribution exceeds that from LIRG already by z~1. A rapid evolution in
both Omega_TIRAGN and Omega_TIRSFG suggests the correlation between star
formation and black hole accretion rate continues up to higher redshifts. We
compare the evolution of Omega_TIRAGN to that of X-ray luminosity density. The
Omega_TIRAGN/Omega_X-rayAGN ratio shows a possible increase at z>1, suggesting
an increase of obscured AGN at z>1.
