This problem is about Line integral of Vector Field. I believe the equation i need to use is: [itex]\int[/itex]F.dr = [itex]\int[/itex]F.r'dt, with r = r(t) I try to solve it like this: C1: r1= < 1 - t , 3t , 0 > C2: r2= < 0 , 3 - 3t , t > C3: r3= < t , 0 , 1 - t > After some computation, I got stuck at the part that have 2 Gaussian Integrals! [itex]\int[/itex](t from 0 -> 1) [-3t + 3t^2 + e^(t^2) - e^[(t-1)^2]]dt I see the answer is 1/2. I check my integrals and observe somehow these 2 Gaussian either cancel out or both equals 0, but I just have no clue how to show it. Another idea I could think of is that there is other way to solve this problem without involving doing those integrals. Thanks for checking out my problem.