System Integration is a term that I'm starting to hear less often. On most of the commercial projects that I work on, system integration is more of the expectation and not necessarily a specific trade or skill that is sought out. Like when I bid on an access control system job, they send me the RFP with the expectation that the fire alarm will unlock all of the doors in the event of a fire and it will stop unauthorized people from getting on the elevator. Somehow that type of integration is taken for granted as a given and nobody sits down and says, "We need to call in a system integrator to make all of this stuff work efficiently and sensibly as possible.
The fire alarm guy is pretty much in the same situation. He isn't called a system integrator per-sé yet he has his meat hooks in just about every other system in the building. The fire alarm is tied into the elevators, the exhaust fans, the door locks, the building audio system, the phones, and the coffee maker if the fire marshal deems this necessary.
There are a lot of system integration contractors out there but I don't know if any of them are doing that as their primary scope of work.