After giving a proposition which reduces the problem of computing the integral closure of a general noetherian ring to the three problems: Compute a universal denominator d (element in the conductor). Compute radical of the ideal generated by d. Compute ideal quotients. We show that for the common case of affine domains, i.e. domains which are finitely generated over fields, of characteristic zero, we can use an effective localization in order to perform most of the computation in one dimensional rings where it can be done with linear algebra.