What is the integral of sine of x square?

Answer 1

It seems you can't express it in terms of the standard functions used in basic calculus; the site Wolfram Alpha (input: integral sin x^2) lists the integral in terms of a so-called Fresnel function. It also lists the first terms of the infinite series.

Answer 2

sin2 x = 1/2(1 - cos 2x)

⇒ ∫sin2 x = ∫1/2(1 - cos 2x)

= x/2 - 1/4 sin 2x + c