In $ ( \mathbb{R^2} ,d_{1})$ find the diameter of the set$ \left\{ (x,arcsinx ) \mid x \in [-1,1] \right\} U \left\{ (-y^2,y) \mid y \in [0,2] \right\}$
I tried dividing it into cases and it's easy when x and y are both elements of the first set or the second in the union, but I have a problem finding the supremum of the distance between$ ( x, arcsinx)$ and $(-y^2,y)$ for $ x \in [-1,1] $ and $ y \in [0,2]$