(Solved): 1. (15 points) Evaluate the line integral \( \int_{C}\left(e^{x}+y^{2}\right) d x+\left(e^{y}+x^{2} ...

1. (15 points) Evaluate the line integral \( \int_{C}\left(e^{x}+y^{2}\right) d x+\left(e^{y}+x^{2}\right) d y \), where \( C \) is the arc of the parabola \( y=x^{2} \) from \( (0,0) \) to \( (1,1) \) and then from the line \( y=x \) at \( (1,1) \) back to the origin.