Integration with Trigonometric Functions

Calculus Level 3

Given \(\displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}\), where \(a, b\) and \(c\) are positive integers and \(b\) and \(c\) are coprime, what is the value of \(a + b + c\)?

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