An odd integral

Calculus Level 5

The image above shows the graph for \(f(x) =\dfrac { { x }^{ 2 } }{ { x }^{ 4 }+4 }\). By drawing a tangent line at either absolute maximum for \(f(x)\), one can bound a finite region above \(f(x)\) that ends at the \(y\)-value for these maxima.

What is the area of this region?


This problem is original. The picture of the graph was produced from Desmos.
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