The improper integral converges if the limit exists; otherwise, it diverges. If the function is continuous on the interval [a,[infinity]), then ∫ₐ[infinity] f(x)dx=lim_(b→[infinity])∫ₐᵇ f(x)dx.

What is the condition for the improper integral ∫₀[infinity] e(-x²) dx to converge?
a) a > 0
b) a ≥ 0
c) a < 0
d) a ≤ 0