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We analyze the computational feasibility of checking temporal integrity constraints formulated in some sublanguages of first-order temporal logic. Our results illustrate the impact of the quantification on the complexity of this problem. The presence of a single quantifier in the scope of a temporal operator makes the problem undecidable. On the other hand, if no quantifiers are in the scope of a temporal operator and all the quantifiers are universal, temporal integrity checking can be done in exponential time.