Let $A\subset \mathbb{R}^{n+m}$ be a compact subanalytic subset. Let $F\colon A\to \mathbb{R}$ be a function which is a restriction to $A$ of a real analytic function defined in a neighborhood of $A$.
Define the function $f\colon \mathbb{R}^m\to \mathbb{R}$ to be the marginal of $F$, i.e. $$f(y)=\int_{A\cap \{ \mathbb{R}^n\times y\}} F(x,y)dx.$$
Is it true that $f$ is real analytic outside of some subanalytic subset of positive codimension?
