The Integration Management Knowledge Area has atleast 1 process in each process group, with a total of 6 processes.
The PMBOK Guide (Fifth Edition), on page 49 lists the chart of knowledge areas to process group interactions.
In terms of real usage of these processes in your projects, PMI says that these 47 processes are just a guideline. They are not mandatory, and it is up to you, as a project manager, to choose which of the 47 processes are required, and which are not required on your project.
Further, you can also decide which inputs, tools and techniques and outputs are you going to use on the projects. Fact is that not all processes are needed or required for each and every project. For example, your own project to improve the customer satisfaction in the company may not need any procurement at all. Many internal IT Projects are not initiated using a Charter. The guidelines suggested by PMI are more of an aspiration… something that you should try to follow as much as possible, within your project constraints, environment and industry.