  We use a four-dimensional lattice calculation of the full-QCD (quantum
chromodynamics, the non-abliean gauge theory of the strong interactions of
quarks and gluons) path integrals needed to determine the masses of the charmed
and bottom baryons. In the charm sector, our results are in good agreement with
experiment within our systematics, except for the spin-1/2 $\Xi_{cc}$, for
which we found the isospin-averaged mass to be $\Xi_{cc}$ to be
$3665\pm17\pm14^{+0}_{-78}$ MeV. We predict the mass of the (isospin-averaged)
spin-1/2 $\Omega_{cc}$ to be $3763\pm19\pm26^{+13}_{-79}$ {MeV}. In the bottom
sector, our results are also in agreement with experimental observations and
other lattice calculations within our statistical and systematic errors. In
particular, we find the mass of the $\Omega_b$ to be consistent with the recent
CDF measurement. We also predict the mass for the as yet unobserved
$\Xi^\prime_b$ to be 5955(27) MeV.
