Nasty areas - 2

Calculus Level pending

Let \[\displaystyle{f(x) = max\{x^2 , (1-x)^2 , 2x(1-x)}\}\],where\(\displaystyle{0 \le x \le 1}\). The area of the region bounded by the curves \[y=f(x),x-axis,x=0,x=1\] can be expressed as \(\dfrac{a}{b}\) . Give \(\displaystyle{a+b}\)

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