Fun with 2015

Calculus Level 4

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

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

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