Answer
it does not matter which curve is chosen.
Work Step by Step
The vector field $F(x,y)=ai+bj$ is known as conservative field throughout the domain $D$, when we have
$\dfrac{\partial a}{\partial y}=\dfrac{\partial b}{\partial x}$
$a$ and $b$ represents the first-order partial derivatives on the domain $D$.
The work integral vector field $W=\int_C \overrightarrow{F} \cdot \overrightarrow{dr}$ is not dependent on the path when $\int_C \overrightarrow{F} \cdot \overrightarrow{dr}=0$ for every closed curve C.
The above statement tells that the work integral gets minimized when the vector field $F$ is conservative, and also, when the curve $C$ is closed.
The curve should have the same initial and last point with respect to its vector function $F(x,y)$.
From the above discussion, we find that it does not matter which curve is chosen.
