Proved that a language is regular

Question

Ι need to prove that this language is regular L = {ab^j c^j | j ≥ 0} ∪ {a^i b^ j c^k | i, j, k ≥ 0 and i /= 1}. I have proved that the first track is not regular with Pumping lemma and the second from the link that I post below: is regular language L ={a^i b^j c^k | i /= 1}. I have come to a dead-end, I cannot understand the result that the connection of a regular and non-regular gives because can be regular or non - regular. Is it possible to tell me some other approach?