Can anybody help me with this problem regarding Line Integrals? Compute ∫F*dr, given the counterclockwise unit circle C : cos((pi)t), sin((pi)t), t∈[0,2] and the vector field F(x, y) = (y²,-x²)

Barrett is comparing the membership fees for two museums. the art museum charges a one-time fee of $8.25 plus $2.25 per month. the science museum charges a one-time fee of $10.75 plus $3.50 per month. how much does barrett save by joining the art museum instead of the science museum?