The trick here is to subdivide this polygon into smaller polygons whose areas are easier to find. To help you get started:
Consider drawing a vertical line thru x=-1. Then you'll have a trapezoid on the left of this vertical line. The area of a trapezoid is
l1 + l2 5+3
---------- * 5. More specifically, A = ------- * 5 = 4*5 = 20 square units.
2 2
On the right side you'll see 2 triangles: One has a height of 4 and a base of 2. The other has a height of 4 and a base of 3. Area of a triangle is (1/2)(base)(height).
Sum up the areas of these three subareas of the original figure.