The area of the shaded region is found by subtracting the area of the semi-circles from the square. The area of the square PQRS with side 1 unit is 1x1 = 1 square unit. The total area of the two semicircles is half the area of a full circle with radius 0.5 units (since Q and S are the centers of the circles and QS is a side of the square). The area of such a circle is pi*(0.5)^2 = pi/4 square units. So, the area of the two semicircles combined is (pi/4)x2 = pi/2 square units.

So, if we subtract the area of the two semicircles from the area of the square, we get: 1 - pi/2 which clearly corresponds to option 4.

Dissolving the other options:

Option 1 is the area of the two semi-circles, but doesn`t consider the square and subtracting the overlapped area. Option 2 is just the half the area of the square. Option 3 isn`t taking two semicircles into account. Hence, none are correct.