Any set of $\mathbb R$ is open iff it is the union of disjoint open intervals

Question

I am starting in my studies on topology and I am having really big troubles with this kind of stuff

I have $(\mathbb R, \tau_u)$, and I have to prove that $A \in \tau_u$ iff $A=\uplus_{i\in I}]a_i, b_i[$

If someone could help me with well-structured demostration of this, I would really appreciate it.