Suppose a curve is described by y = f(x) on the interval [-b, b], where f' is continuous on [-b, b]. Show that if f is symmetric about the origin ( f is odd) or f is symmetric about the y-axis ( f is even), then the length of the curve y = f(x) from x = -b to x = b is twice the length of the curve from x = 0 to x = b. Use a geometric argument and prove it using integration.