Calculate autocorrelation of a sinus
It's way easier to use the complex representation of cosine not involving the real part operator. In your case this translates into expressing

$$ \cos(h(t))=\frac{e^{jh(t)} + e^{-jh(t)}}{2} $$

Note that this yields an autocorrealtion of
$$ R_s(\tau)=\int_{0}^{T_s} \frac{e^{jh(t)} + e^{-jh(t)}}{2}\frac{e^{jh(t-\tau)} + e^{-jh(t-\tau)}}{2} dt $$