It is a very nice point u ask there.This question is very much there in CBSE NCERT text but i think the solution there is wrong .

See the area enclosed between the curves (Parabola and Circle) is asked.

so according to definition ,(Parts of the curves should form the boundary of the area u r going to consider). Here x axis (the way in which the question is worded is not one of the curves).It is just said "area above x axis".So actually u shud consider the small area (almost convex shaped) between the curves,and not the bigger area above x axis.(bcos if u take this then it means u r considering x axis also as one of the curves which is wrong).

 

I think the answer so obtained is 4pi - 32/3