∫₀^∞ e^(−x²) dx converges to √π/2, a finite answer involving π, for a function with no elementary antiderivative. Why does the impossibility of the indefinite integral not block the definite one?

B. Because the definite integral is a limit of areas, not an antiderivative

The integral is defined as a limit of sums and exists whether or not a formula does, the Fundamental Theorem is a convenience, not the definition. This one is evaluated by a polar-coordinate trick in two dimensions, and its value is why the normal distribution's constant contains a √π.