Final answer:
To solve this problem, an integral calculus formula for the area of a surface of revolution is needed. However, the given curve is not defined for real y values over the interval [0,1] which is necessary to compute the area.
Step-by-step explanation:
To find the area of the surface generated by revolving the curve y = √(-x² + 2x - 3) about the x-axis on the interval [0,1], we need to use the formula for the surface area of a solid of revolution, which is an application of integral calculus. Unfortunately, it appears that the curve given in this problem may not have a real solution within the interval [0,1], as the term under the square root needs to be non-negative for real y values.
To proceed with the solution, we would first ensure the curve provides real values, then set up the integral for the surface area, using the formula S = 2π ∫ y ds, where ds is the differential arc length, ds = √(1 + (dy/dx)²) dx. However, without a valid function for y, we cannot compute this surface area.