Curves & Motion · Superchallenge problem

A plane curve starts at the origin heading in the direction of the positive $x$-axis and is traced at unit speed. Its signed curvature (positive means turning left) at arc length $s$ is $\kappa(s) = \dfrac{1}{1 + s^{2}}$. Find the $y$-coordinate of the point reached at $s = \tfrac43$.