Nasty areas!

Calculus Level 5

If the area bounded by the curves \(y = x^2\), \(y= |2-x^2|\) and \(y=2\), which lies to the right of the line \(x=1\) can be expressed as \(\dfrac{a - b \sqrt{c}}{d}\), then what is \(a+b+c+d\)?

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