  Let $SU_X(n,L)$ be the moduli space of rank n semistable vector bundles with
fixed determinant L on a smooth projective genus g curve X. Let $SU_X^s(n,L)$
denote the open subset parametrizing stable bundles. We show that if g>3 and n
> 1, then the mixed Hodge structure on $H^3(SU_X^s(n, L))$ is pure of type
${(1,2),(2,1)}$ and it carries a natural polarization such that the associated
polarized intermediate Jacobian is isomorphic J(X). This is new when deg L and
n are not coprime. As a corollary, we obtain a Torelli theorem that says
roughly that $SU_X^s(n,L)$ (or $SU_X(n,L)$) determines X. This complements or
refines earlier results of Balaji, Kouvidakis-Pantev, Mumford-Newstead,
Narasimhan-Ramanan, and Tyurin.
