(D) for me
The line y=x is at 45° from the X axis. Similarly, y=-x gives also an angle of 45° with the Y axis.
So, the angle between y=x and y=-x is 90° (360°/4).
y^2 + x^2 = 4 = 2^2 represents a circle centered on 0(0,0) and with a radius of 2.
The 2 lines y=x and y=-x interestec on 0(0,0). So, the upper area described is actually 1/4 of the area of the circle definied before.
Thus, we have:
Area = 1/4 * Area of circle
= 1/4 * Pi * 2^2