What is meant by saying that two norms on a real vector space are Lipschitz equivalent?

Show that any two norms on $\mathbb{R}^{n}$ are Lipschitz equivalent. [You may assume that a continuous function on a closed bounded set in $\mathbb{R}^{n}$ has closed bounded image.]

Show that $\|f\|_{1}=\int_{-1}^{1}|f(x)| d x$ defines a norm on the space $C[-1,1]$ of continuous real-valued functions on $[-1,1]$. Is it Lipschitz equivalent to the uniform norm? Justify your answer. Prove that the normed space $\left(C[-1,1],\|\cdot\|_{1}\right)$ is not complete.