TIFR-2018-Maths-A: 4

Question

True/False Question :

Let $f$ be a nonnegative continuous function on $\mathbb{R}$ such that $\int_{0}^{\infty }f\left ( t \right )dt$ is finite. Then $\underset{x\rightarrow \infty }{lim}\:f\left ( x \right )=0.$