Remove peeling paint or paint over it ??

[Boodi]

I'm in the process of decorating my front room and there are 4 alcoves that were papered which I have removed the paper easily with a paper stripper however some paint from underneath the paper has peeled off. Under the paint is back to the original plaster (in good condition) but I'm not sure what the best thing to do next.... Do I take the paint off completely and start over again or do I use a filling paint to cover up the peeled parts ?? Any advise would be great as I'm brand new to this !! (Also I'm unsure if the plaster was ever primed ?! I'm not sure if there is a way to tell this as there is no sign of anything under the paint currently on there)

Thanks

 

[sparkwright]

Either way sounds ok, as long as the loose stuff is scraped off.