First quadrant= x>0 and y>0 ie as above.
Enclosed by arcs just means the arc(curve) is the boundary.
You need to find the intersection point of the two curves, this is point p and here x=√𝑎𝑐
A2 is the area under the blue curve, 𝑦 2 = 𝑎𝑥 between o and point p.
A1 is the area under the other curve from x=0 to P and the integration is as per the schedule.