Evaluate the integral in terms of areas. I understand that the first one is 4 from basically adding the squares inside the signed area, but I'm unsure on how to proceed in getting the other integrals. Any help would be appreciated, thank you.
Some tricks to help you:

a. count squares

b. calculate the area of known figures, such as triangles and rectangles.

For example, the integral in (b) can be calculate as the same of the area of a trapezoid($(1+3)\cdot 2/2$), a rectangle ($1\cdot 3$), and a triangle ($3\cdot 2/2$) to give a grand total of $10$.

That should cover it, good luck.
see the solution on your graph