Traditional methods for integrity checking in relational or deductive databases heavily rely on the assumption that data have integrity before the execution of updates. In this way, as has always been claimed, one can automatically derive strategies to check, in an incremental way, whether data preserve their integrity after the update. On the other hand, this consistency assumption greatly reduces applicability of such methods, since it is most often the case that small parts of a database do not comply with the integrity constraints, especially when the data are distributed or have been integrated from different sources. In this paper we revisit integrity checking from an inconsistency-tolerant viewpoint. We show that most methods for integrity checking (though not all) are still applicable in the presence of inconsistencies and may be used to guarantee that the satisfied instances of the integrity constraints will continue to be satisfied after the update.