Consider the vector field F = (x^2 - y^2)i + (y^2 - Z^2)j + (z^2 - x^2)k.

a) Calculate the line integral of F from P_0 at (1,0,0) to P_1 at (-1,0,0) along the direct line path joining these points.

b) Calculate the line integral of F from P_0 at (1,0,0) to P_1 at (-1,0,0) along the horizontal semicircular path joining these points, traversed anti-clockwise (through the point (0,1,0)), which forms part of the circle centred at the origin. You may need to use sin^3t = sint(1-cos^2t).