A Very Odd Integral

Calculus Level 3

\[\large \int _{ -{ \pi }/{ 4 } }^{ { \pi }/{ 4 } }{ \, x^3 \sec^2{x} }~ {dx} \]

If the integral above is equal to \(\pi^A -B\), where \(A\) and \(B\) are integers, find \(A+B\).

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