Need help proving that an indicator/characteristic function on a closed interval [a,b] belongs to an $L^p$ space

Question

For any $a,b$ real numbers with $a<=b$ and for any $p\in[1,\infty)$ I want to show that

$1_{[a,b]}\in L^p$

Now, I have a basic understanding of $L^p$ spaces and understand what a characteristic function looks like but I don't know how to prove this formally/by the book.