Convexity of a set defined by integrals of a function on measurable sets

Question

While studying measurable function, I want to know if the following statement is true. Let $\mu$ be a measure on $\mathbb R^n$ with a support with nonempty interior, $f$ polynomial function and $B$ a compact subset of $\mathbb R^n$ : $$A = \left\{\int_{\Omega} f \mathrm d\mu : \Omega \subset B \text{ $\mu$-measurable}\right\}$$ is convex. Can any one help me to prove or disprove this statement ?