Chapter 17.3, Problem 44E

Using the Fundamental Theorem for line integral verify that the fundamental Theorem for line integrals can be used to evaluate the given integral, and then evaluate the integral.

44. ${\displaystyle \underset{C}{\int }}$ e^xy dx + e^x dy, where C is the parabola r(t) $\langle t+1,t^2\rangle$, for −1 ≤ t ≤ 3