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The area of the region described by $\;A=\{(x,y) : x^{2}+y^{2} \leq 1 \;and\; y^{2} \leq 1-x\}\;$ is :

$(a)\;\large\frac{\pi}{2} - \large\frac{2}{3}\qquad(b)\;\large\frac{\pi}{2} + \large\frac{2}{3}\qquad(c)\;\large\frac{\pi}{2} + \large\frac{4}{3}\qquad(d)\;\large\frac{\pi}{2} - \large\frac{4}{3}$

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