A bit off tangent (My sixteenth integration problem)

Calculus Level 3

\[\large \displaystyle \int_{0}^{1} \dfrac{1-x^{2}}{1+x^{2}} \, dx \]

If the above integral can be expressed in the form

\[ \dfrac{a \pi}{b} - c \]

where \( a, b, c\) are positive integers and \(a, b \) are coprime, find \(a+b+c\).

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