The problem of information integration is important for upgrading a search engine to a question-answering system. In the paper we consider a new fuzzy spectral approach to information integration in a search engine. The approach employs a series of variance-covariances matrices and suggests the eigenvalue spectra of the matrices as important characteristics of information integration. We show that the characteristics can be described in terms of eigenvalue dynamics. Through computational experiments we have identified an eigenvalue dynamics that can be efficiently computed by using the quadratic trace of the variance-covariance matrix. Moreover, this dynamics shows a property that can be interpreted as the eigenvalue integration. This suggests that the spectral characteristics are connected with an integration mechanism. The fuzzyfication of eigenvalues plays a key role in the observation of the dynamics. This may support the idea that fuzziness is an integral part of information integration.