1. An information integrating apparatus, comprising: a memory; and a processor coupled to the memory and configured to execute a process including: storing, into the memory, meta-definitions that include physical models, logical models, and a mapping definition, the physical models being data models on an information source side, the logical models being data models on a user-side that uses integrated information, the mapping definition indicating corresponding relations between the physical models and the logical models; executing a first integration process that integrates information from the physical models and information from the logical models by referring to the mapping definition; executing a second integration process that includes a breaking up process and a collection process, the breaking up process breaking up a query for the logical models into a query for the physical models by referring to the mapping definition and the collection process collecting retrieved information by the query for the physical models; detecting a first instruction from the information source side or a second instruction from the user side, the first instruction being an instruction to integrate, by the first integration process, information from the physical models, and the information from the logical models, into a first integration result, the second instruction being an instruction to integrate, by the second integration process, the information from the physical models and the information from the logical models into a second integration result; controlling the first integration process, when the detecting detects the first instruction or the second integration process when the detecting detects the second instruction; outputting to the user-side, the first integration result when the detecting detects the first instruction, or the second integration result when the detecting detects the second instruction, wherein the processor is configured so that the controlling, when an unsolved mapping definition is present in the first integration result, further generates a third integration result by referring to the unsolved mapping definition, the physical models and the logical models, controls the breaking up process, the collection process and the first integration process and the second integration process, and executes the breaking up process on a query for the logical models on the user-side, the collection process with respect to information other than the query that is for the physical models and obtained by the breaking up process, and the first integration process and the second integration process on the information from the physical model collected by the collection process, and the outputting further outputs to the user-side, the first integration result and the third integration result, when an unsolved mapping definition is present in the first integration result.