drwho

I am trying to clear something that seems to be a little misleading for me. I know the language over {a,b} consisting of all words containing the same number of occurrences of the symbol a as of the symbol b is not regular. I know that the language L over {a,b} consisting of all words containing the same number of occurrences of ab as a substring as occurrences of ba as a substring actually is regular. What would be the best way to prove this? by finding a finite automaton that accepts this language?