Distributed information retrieval searches information among many disjoint databases or search engine results and merge of retrieved results into a single result list that a person can browse easily. How to merge the results returned by selected search engine is an important subproblem of the distributed information retrieval task, because every search engine has its own calculation or definition about relevance of documents and has different overlap range. This article presents a fuzzy integral algorithm to solve the merging results problem. We have also a procedure for adjusting fuzzy measure parameters by training. Compared to the method of relevance scores fusion and Borda count fusion, our approach has the excellent ability to balance between chore effects and dark horse effects. The experiments on web show that our approach gets better ranked results (more useful documents on top ranked).