I suggest you find the area of the 3 cm radius sector, then subtract this area from the 3 by 3 square to get the unshaded area.

Do the same for the 2 cm radius sector.

Then, find the area of the semicircle with radius 1 cm, subtract that from the square with sides 2 by 2 to get the unshaded area.

now, you only have to find the last unshaded area, at the top right corner. Find the area of the segment with 1 cm radius, subtract that from the 1 by 1 square.

Add all the unshaded areas together, then subtract that from the total area of the rectangle with area 4 by 3.