That is great news! Thanks Northwind. I tried pulling the bearing out, but it seems to be held fast. Should I keep tugging or is it worth getting one of the cup removal tools instead please?
If your frame really is integrated, the bearings literally just sit on a ledge machined into the headtube. There are no cups to remove. Chances are that there's just a bit of corrosion part seizing the bearings into the headtube. If it were me, I'd soak the area with Plus Gas or WD40 overnight and then try taking the bearings out again by hand or maybe, very carefully with some sort of suitable lever if there's a ledge you can get it under and there's no chance of damaging the frame. Don't lever directly against the end of the headtube etc, it's common sense really.
Once you've done that, installing a new integrated headset is super easy, you just pop the bearings in, replace everything in the right order and adjust correctly.
You should also check the spec carefully, there are a few integrated bearing standards around. What frame is it?