$f:\mathbb{R} \rightarrow[0,\infty) $ is a measurable function, if $\int_{-\infty}^{\infty} f(x)=1$, then $\int_{-\infty}^0\frac{1}{1+f(x)}=\infty$
Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$