Integrate the unknown function please

Calculus Level 5

Let \(g\left( x \right)\) be a quartic (\({ 4 }^\text{th}\) degree) polynomial such that \(g\left( n \right) ={ n }^{ 3 }-{ 2 }^{ n }\) for \(n=0,1,2,3,4\).

Find

\[45\int _{ 0 }^{ 4 }{ g\left( x \right) dx } \]

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