Integration with Trigonometric Functions

Calculus Level 3

Given 03π2x2cosxdx=abπ2c\displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}, where a,ba, b and cc are positive integers and bb and cc are coprime, what is the value of a+b+ca + b + c?

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