This paper introduces an adaptive method that can be used to construct the query user interfaces for the information integration systems (IIS) on the Web, and a constraint-based method for mapping queries from such IISs into the specific formats of heterogeneous Internet sources. The fuse of this research was ignited by witnessing that WWW information searching becomes harder and harder due to the tremendous development of the Internet and the explosive growth of digital information on the World Wide Web. Incorporating adaptive and constraints-coordinated mechanisms into an information integration system can overcome the diversity of heterogeneous sources and utilize the functionality of the individual sources to the fullest extent.