  We construct a long exact sequence involving the homology of an FI-module.
Using the long exact sequence, we give two methods to bound the
Castelnuovo-Mumford regularity of an FI-module which is generated and related
in finite degree. We also prove that for an FI-module which is generated and
related in finite degree, if it has a nonzero higher homology, then its
homological degrees are strictly increasing (starting from the first
homological degree).
