A thin, rigid wire carries a steady current \(I\) in the \(xy\)-plane along the parabolic path \(y = kx^2\) from the origin \((0,0)\) to the point \((L, kL^2)\), where \(k\) and \(L\) are positive constants. The current flows along the wire in the direction of increasing \(x\). A non-uniform external magnetic field perpendicular to the \(xy\)-plane is given by \(\vec{B}(x) = B_0 \left(\dfrac{x}{L}\right) \hat{k}\), where \(B_0\) is a positive constant and \(\hat{k}\) is the unit vector pointing in the \(+z\)-direction. Which of the following integral expressions correctly represents the net magnetic force vector \(\vec{F}\) exerted on the wire?