By connecting various points in the figure, we have the following:
It is obvious that the radius of each quarter circle is $\dfrac{\sqrt{2}}{2}$, and the area of two green regions is: $$\dfrac{1}{2}-\dfrac{1}{4}\cdot\pi\cdot(\dfrac{\sqrt{2}}{2})^2=\dfrac{1}{2}-\dfrac{\pi}{8}$$ Therefore, the total area of the blue regions is equal to the area of the unit square minus 4 times of the area of the two green regions: $$1-4\cdot(\dfrac{1}{2}-\dfrac{\pi}{8})=\dfrac{\pi}{2}-1$$