Evaluate the line integral \( \oint_C y^3 dx + (3xy^2 - 2x) dy \) where C is the closed curve consisting of line segments from (0,0) to (4,0), from (4,0) to (2,2), from (2,2) to (1,2), from (1,2) to (0,0).
(Note: the closed curve is in counter-clockwise direction/positively oriented.)