A thin circular wire of radius \(R\) lies in the \(xy\)-plane centered at the origin. A steady current flows counterclockwise around the wire such that the current magnitude as a function of the azimuthal angle \(\theta\) (measured counterclockwise from the positive \(x\)-axis) is given by \(I(\theta) = I_0 \cos^2\theta\), where \(I_0\) is a positive constant. Which of the following expressions represents the correct integral setup using the Biot–Savart law to determine the magnetic field vector \(\vec{B}\) at the origin?