Gram-Schmidt Or?

Calculus Level 5

\[ \large \int_{-1}^1 \Big|x^3 - a-bx - cx^2\Big|^2 \, dx \]

Let \(a,b,\) and \(c\) be real constants.

If the minimum value of the integral above can be expressed as \( \dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

\[\]Notation: \( | \cdot | \) denotes the absolute value function.

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