  We consider the cosmological models for the higher dimensional spacetime
which includes the curvatures of our space as well as the curvatures of the
internal space. We find that the condition for the integrability of the
cosmological equations is that the total space-time dimensions are D=10 or D=11
which is exactly the conditions for superstrings or M-theory. We obtain
analytic solutions with generic initial conditions in the four dimensional
Einstein frame and study the accelerating universe when both our space and the
internal space have negative curvatures.
