Integrate with series

Calculus Level 5

If \(\large{f(x)=\displaystyle \sum^{\infty}_{n=0} \frac{(-x^2)^n}{(2n+1)!}}\) such that the equation below is true for integers \(A\) and \(B\), find the value of \(A+B\).

\[\large{\displaystyle \int^{\frac{\pi}{2}}_{0} f(x)f\left (\frac{\pi}{2}-x \right )dx=\frac{A}{\pi^{B}}\displaystyle \int^{\pi}_{0} f(x) dx}\]

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