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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