  The concept of integro-differential algebra has been introduced recently in
the study of boundary problems of differential equations. We generalize this
concept to that of integro-differential algebra with a weight, in analogy to
the differential Rota-Baxter algebra. We construct free commutative
integro-differential algebras with weight generated by a base differential
algebra. This in particular gives an explicit construction of the
integro-differential algebra on one generator. Properties of these free objects
are studied.
