Integrated training means that everything you do is linked together with meaning.
When I first started training I couldn't correlate the movements of basics/kata with what we did in self defense class, with what we did in sparring. The three activities were all different. It was as though we were learning three different things - robot dancing, pre-arranged techniques and sparring.
What was missing was a relationship between all areas of training. For example we would do upper block - yet nobody used the text-book upper block in sparring or any other situation. Perhaps we didn't understand the nature of the beast, and from the sparring point of view it was all competition based (WTF taekwondo rules, the yawn-fest that is now in the Olympics.)
I was discussing this the other night in the dojo. There has to be a link bringing together kata, basics, pairs work, and everything else. To paraphrase - "A collection of techniques and exercises is no more a martial art than a pile of bricks is a house".
So in training how can you relate what you do on focus mitts to how you work your basics? How does kata come into it? What kind of sparring is required to get the results you need? Do you use any other training methods? Is everything integrated into a complete picture - or are you just moving from one room to another without any real thought?
Kata - Kumite - Kihon are all aspects of the same thing. It is important not to get stuck in the terminology of it. Kata is whatever you make it, Kihon represents your fundamentals and Kumite means any interaction with another person, not just bouncing around exchanging reverse punches....
Train them in different ways, but keep everything together.