Cofiniteness of local cohomology modules and subcategories of modules

Let R be a commutative noetherian ring and I an ideal of R. Assume that for all integers i the local cohomology module H-I(i) (R) is I-cofinite. Suppose that R-p is a regular local ring for all prime ideals p that do not contain I. In this paper, we prove that if the I-cofinite modules form an abelian category, then for all finitely generated R-modules M and all integers i, the local cohomology module H-I(i) (M) is I-cofinite.