The Attempt at a Solution
The only thing you are doing wrong is that you have not finished the problem!
You have (9- 12+ 4)- (1/4+ 1- 1). Okay, what number is that?
You're right, it is a conservative field - that's the key to the solution.
I think you're trying to use path independence, which is also key, but try it another way.
you're looking for the integral of F; and F = grad f... well... what's the integral of grad f?