Let $F(\mathbf{x}) \in \mathbb{Z}[x_1, ..., x_n]$ be a degree $d$ homogeneous form. Let $$ I(\alpha) = \int_{[0,1]^n} e^{2 \pi i F(\mathbf{x}) \alpha} dx_1...dx_n. $$ Then the singular integral is defined as $$ \sigma_{\infty} = \int_{\mathbb{R}} I(\alpha) d\alpha. $$

It says in an article I am reading that $\sigma_{\infty} > 0$ if the equation $F(\mathbf{x}) =0$ has a non-singular real solution in $(0,1)^n$. I would greatly appreciate if someone could give me a hint or some explanation on how I can prove this statement. Thank you very much.