Prove that if \(F(x)\) is a distribution function, then for any \(h eq 0\) the functions

\[ \Phi(x)=\frac{1}{h} \int_{x}^{x+h} F(x) d x, \quad \Psi(x)=\frac{1}{2 h} \int_{x-h}^{x+h} F(x) d x \]

are also distribution furictions.