nowhere $0$ vector field on $\mathbb{R}$ such that integral curves can be defined only on neighborhood of $0$

Question

This is question 2 from Spivak Vol 1. Chapter 5:

Find a nowhere $0$ vector field on $\mathbb{R}$ such that all integral curves can be defined only on some interval around $0$.

I don't quite understand what the question is asking...

Is $x \mapsto (x^2 + 1)\partial /\partial x$, with integral curve $t \mapsto t^3/3 + x$ a solution?