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

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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