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$\large \begin{cases} {f(1729) = 4} \\ {f(1730) = 5} \\ {f(1731)=6} \\ \end{cases}$

Let $f(x)$ be a cubic polynomial satisfying the following system of equations. Find $\displaystyle\int _{ 1729 }^{ 1731 }{ f(x)dx }$.

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