A thin, nonconducting wire carrying a uniform positive linear charge density \(\lambda_0\) is bent into a planar spiral described in polar coordinates by \(r(\theta) = b\theta\) for \(\pi \le \theta \le 2\pi\), where \(b\) is a positive constant. The spiral lies in the \(xy\)-plane with the origin \((0,0)\) located at \(r = 0\). Which of the following expressions correctly represents the integral set up to determine the \(y\)-component of the net electric field, \(E_y\), at the origin?