What is "integrity" and how is it different from hull? Is this a new feature? I never saw such a stat.
As far as I know 'integrity' has been in the game from the start. It differs from 'damage'. A simple (ish) explanation of it might be easier if I used an example of a car (for those that own one!).
If you buy a brand new car everything will be top notch and all parts should work perfectly. However, if some idiot opens their car door against the side of your car and dents it, that is 'damage'. Or if you reverse into a post and break your rear bumper (fender), that is also 'damage'. If someone shoots at you and put s a bullet hole in it that is also damage! All those can be repaired as and when necessary.
However, as you use your car, certain parts begin to wear, like perhaps the timing belt, brake pads, electric window winders (if you have them!), and after a while some items may develop a fault, perhaps a dodgy wire to the radio, that causes it to cut in and out, that sort of thing. That is why cars should be serviced and maintained. If your oil gets very old and isn't changed for a long time, the engine wears more, and may not perform as well as it used to. If the timing belt is allowed to wear out and is not replaced before it breaks, this can be fairly catastrophic for the engine! All those sort of things are what we know of as 'general wear and tear', or in Elite Speak as 'integrity'.
As things wear or even wear out, if not checked regularly, and replaced when deemed necessary, the vehicle will begin showing faults (warning lights come on, that sort of thing!) and won't perform as expected ... or at all!
So, whether it's you car or for your Cobra (or whatever) the motto is: Keep it well serviced and maintained!