Sequence where $\lim_{k\to\infty}f_k(x)=0$, but $\lim_{k\to\infty}\int f_k(x) d\lambda=1$

Question

Is there an example of a sequence of simple, Borel measurable sets from $\mathbb{R}$ to $[0,\infty)$ such that $\lim_{k\to\infty}f_k(x)=0$ for all $x\in \mathbb{R}$, but $\lim_{k\to\infty}\int f_k(x) d\lambda=1$.

I'm a little confused on how to construct a sequence like this. Would it have something to do with the characteristic function perhaps?