300 followers problem

Calculus Level 5

Let $${ f(x) = \text{max}\left\{ { x }^{ 2 },{ \left( 1-x \right) }^{ 2 },2x(1-x) \right\} }$$.

Determine the area of the region bounded bt the curves $$y=f(x)$$, $$x$$-axis, $$x=0, x=1$$.

If the area is of the form $$\frac a b$$ for coprime positive integers $$a,b$$, find $$a+b$$.

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