Given that $u$ is twice continuously differentiable real-valued harmonic function on a disk $D(z_o;r)$ centered at $z_o=x_o+iy_o$, show that the equation, $v(x_1,y_1)=c+\int_{y_{0}} ^ {y_{1}}\frac{\partial u}{\partial x}(x_1,y)dy-\int_{x_{0}} ^ {x_{1}}\frac{\partial u}{\partial y}(x,y_0)dy$, defines a harmonic conjugate for $u$ on $D(z_o;r)$ with $v(x_o,y_o)=c$.
I don't know how to go about proving this, my initial intuition says to work with the Cauchy-Riemann equations but I'm really confused with what the question wants. Can someone carefully explain this question to me so that I understand what I'm supposed to do? Would the Fundamental Theorem of Calculus have something to do with this, that is, take the partial of $v(x_1,y_1)$ with respect to both x and y?
Use the Fundamental Theorem of Calculus to show that for u and v the Cauchy-Riemann equations are valid.