Orthogonal polynomials symmetric about centre of interval

Question

Let $\omega(x)$ be an even weight function and $[-a,a]$ a symmetric interval about $0$. How can I prove that the orthogonal polynomials with respect to this weight function satisfy $\phi_k(-x)=(−1)^k\phi(x)$ for $k=1,2,3,...$? I have done a $y=-x$ substitution in the integral but not sure where to go from there.