Let (T t ) be a C 0 semigroup with generator A on a Banach space X and let A be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ, A) of A belongs to A if and only if the integrated semigroup S t := t 0 T s ds belongs to A. For analytic semigroups, S t ∈ A implies T t ∈ A, and in this case we give precise estimates for the growth of the A-norm of T t (e.g. the trace of T t ) in terms of the resolvent growth and the imbedding D(A) → X.