Let $f:\mathbb{R}\to \mathbb{R}$ be a continuous function such that $$f(x+1)=\frac{1}{2}f(x)\mathrm{\forall }x\in \mathbb{R},$$ and let $a_n={\int }_0^{n}f(x)dx$ for all integers $n\ge 1.$ Then $$\underset{n\to \mathrm{\infty }}{lim}{a}_n\text{exists and equals}2{\int }_0^{1}f(x)dx.$$