Evaluate the following line integrals using the appropriate method. State any fundamental theorems that you use in your answers.

a. Integral of F dot dr where F(x, y) = and C consists of the arc of the curve y = cos x from (-pi/2, 0) to (pi/2, 0) followed by the line segment from (pi/2, 0) to (-pi/2, 0).

b. Integral of F dor dr where F(x, y) = and C is the curve starting at (0, 0), going to the point (2, 0) along the x-axis, and then going around the circle x^2 + y^2 = 4 to the point (sqrt(2), sqrt(2)).