Sending the Poincaré dual class of a point in a smooth manifold to 1

Question

I have been given the following problem:

For a compact oriented $n$-dimensional manifold, use a nowhere zero $n$-fold $\omega\in\Omega^n(M)$ to define a linear map \begin{equation} [M]: H^n(M)\to \mathbb{R} \end{equation} sending the Poincaré dual class $\eta_{\{x\}}$ to 1 for each $x\in M$

Good someone give a pointer or two?