Closed form of integral $\int_a^b e^{-ix^2} dx$

Question

Does any know how to find the closed form of integral $\int_a^b e^{-ix^2} dx$ for any real $a$ and $b$. It seems that I need to use the fresnel integrals.

Answer 1

$$\int_a^b e^{-ix^2} dx = \int_a^b \cos x^2 dx - i\int_a^b \sin x^2 dx$$