Recently I learned functional integral's formalism in quantum field theory. I have realized that I don't understand why exactly do we introduce it. We have the expression for $S$-matrix, then we may rewrite it in through functional integral.
But why do we use functional integration? I read that it helps to "conserve" gauge symmetries for massless fields and that it avoids infinite results after integration through internal lines. But these are formal arguments. I don't understand it clearly.
Can you add some information which can help me?