Fun with 2015

Calculus Level 3

{f(2013)=3f(2015)=1f(2017)=5f(2019)=2015 \large \begin{cases} {f(2013) = 3} \\ {f(2015) = 1} \\ {f(2017)=5} \\ {f(2019)=2015} \\ \end{cases}

Given that a cubic polynomial f(x)f(x) that satisfy the system of equations above, find the value of 20132017f(x)dx \displaystyle \int_{2013}^{2017} f(x) \, dx .

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