Given below are two statements:
Statement $I$: An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $\vec{F}$. The work done by the force is $W = -\int_{r_{1}}^{r_{2}} \vec{F} \cdot d\vec{r}$.
Statement $II$: Any object moving from one location to another location can follow an infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below:

• A
  Both Statement $I$ and Statement $II$ are true
• B
  Statement $I$ is false but Statement $II$ is true
• C
  Statement $I$ is true but Statement $II$ is false
• D
  Both Statement $I$ and Statement $II$ are false