We introduced integrals over parameterized curves. We first gave an intuitive definition patterned after the Riemann integral of functions of a real variable, then a formal definition using the derivative of the parameterization function. We discussed invariances of the integral, in particular under a change of the parameterization. We also gave two upper bounds on the absolute value of an integral, one based on the intuitive definition, and one on the formal definition of the integral. HW: 38,39,42,43.