is the statement true/false.
Let $f$ be a continuous integrable function of $\mathbb{R}$ such that either $f(x) > 0$ or $f(x) + f(x + 1) > 0$ for all x$ \in \mathbb{R}$. Then $\int_{-\infty}^{\infty} f(x)dx>0$
is the above statement is true please help someone.
i am sorry that i could not wright it properly.the ingration will be from -infinity to infinity.thanks for help.