you can physically put HID kits on any type of headlights except for maybe sealed beams applications but you need not to worry about that.
HID kits contain a xenon gas "High Intensity Discharge" bulb, a ballast to ignite the bulbs. and some wire harnesses to hook up to your stock wire harness.
all you really need to do is select the correct bulb for your application and like i said there HID kits for almost all applications of bulbs. cause that's all it really is to fitting them into headlights.
now stock DA headlights use 9004 bulbs which is considered a dual filament bulb which has both high and low beam on one bulb.
some HID kits only offer 9004 in low beam... some offer them in high and low. but expect to pay for that.
usually you'll see it written as "9004H/L"
now a last note is that stock headlights for the integra are not really meant for HID. what i mean by that is the headlight optics are meant for halogen bulbs. with the extra intensity of HID its going to translate into added glare. not only that but its also considered illegal to retrofit to HID.
do cops really bother you? not really unless you get silly colors like deep blue, pink, purple, or green...
as long as you buy a HID kit with a kelvin rating of 4000k - 6000k you'll be fine and between this range you'll get the best light output anyways.