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Calculus Level 4

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

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