Find the potential of a given vector field at a point - getting expressions I can't compute.

Question

the given vector field $$\vec{F}(x,y) = \frac{(x-y)\hat{i} + (x+y)\hat{j}}{x^2 +y^2}$$ has a potential function $U(x,y)$ that is defined in $D=\{(x,y): 1\leq x^2 + y^2 \leq16,\: y\geq 0\}$. and it's given that $U(3,0) = 0.25\pi$ - find $U(-3,0)$
my approach and the problem with it:
I've tried integrating to find the potential function and then finding the constant by placing the given point in it. The problem is that I got expressions that I can't compute. $$U = \int \frac{(x-y)}{x^2 +y^2} dx = -arctan\left(\frac{x}y\right) + \frac{1}2ln\left(x^2 +y^2 \right) + h(y) $$ derived and compared $U_y$ with the $\hat{j}$ component and got: $$ h'(y) = 0 \Rightarrow h(y) =c $$ now to find C i needed to input $(3,0)$ but this gets me as a part of the calculations to compute $-arctan\left(\frac{3}0\right)$ - I don't know how to procceed... I tried assuming $0=0+$ because of D I know y can't be lesser than $0$ but that got me a wrong result. The final answer should be $$U(-3,0) = 0.75\pi$$ is my approach correct? where am I wrong? is there an easier way? edit: A different - better - approach uses FTC instead, I don't completely understand it and the person who proposed it got the wrong result as well... If you can do it with that, explain it and get it right that'd be awesome.