even though I suspect that there will be many definitions based on personal preferences, there has been a comprehensive article written by Dr. Pamela Peeke and published here are IDEA which makes a very good case. It is rather long, and I am providing a link http://www.ideafit.com/fitness-library/the-new-science-of-body-mind-medi….
Mr. Bell, Integrative Fitness can be interpreted and described in various ways, depending upon the Practitioner.
My company would describe it by stating that we incorporate Varying Training Modalities (Metabolic ReStart, Strength, Endurance, Speed, Agility, Stability, Coordination, Balance, Flexibility, Cardio Enhancement, Functional Performance, etc.) into the program.
As a Nurse, I also apply the studies of Naturopathy and Alternative Healing Methods, when applicable.
Let me know if you would like additional info.
To Your Health!