  The object of the present study is the integrated density of states of a
quantum particle in multi-dimensional Euclidean space which is characterized by
a Schr\"odinger operator with a constant magnetic field and a random potential
which may be unbounded from above and from below. For an ergodic random
potential satisfying a simple moment condition, we give a detailed proof that
the infinite-volume limits of spatial eigenvalue concentrations of
finite-volume operators with different boundary conditions exist almost surely.
Since all these limits are shown to coincide with the expectation of the trace
of the spatially localized spectral family of the infinite-volume operator, the
integrated density of states is almost surely non-random and independent of the
chosen boundary condition. Our proof of the independence of the boundary
condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and
T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal.
{\bf 173} (2001) 136-152].
