Line integrals over smooth curves

Question

While learning the concept of a line integral over a curve, I was told that the curve over which the line integral is to be computed has to be smooth. The line integral is given by, $\int_{a}^{b} f(x, y, z) |\vec{v(t)}| \mathrm dt$. Does the condition "smooth curve" arise from the fact that velocity $\vec v(t)$ is undefined at sharp turns and jumps?