Explanation:

Correct Answer is (a).In the bold part the relative pronoun 'which' must be replaced by 'that' as the clause following the word 'which' is restrictive and not descriptive. 
Next, the correct phrasal verb in the context is 'break out' which means 'to start suddenly' specifically in case of war, fighting, or similarly undesirable things.
Further, 'in' will be a better preposition than 'across' in the context.
Clearly, the sentence after replacements, will be:
The conflict that broke out in the oil-rich city of Kirkuk is a reminder of the divisions that run deep in the country.Hence, option A is the correct answer.