Wait, That's Not Integrable!

Calculus

$\int_{0}^{1}\sin x^2 \, dx$

Which of the following series can be expressed as the value of the integral above?

Hint: Take its Maclaurin series.

\sum_{n = 0}^{\infty} \frac{(-1)^n}{(4n + 3)(2n + 1)!}

\sum_{n = 0}^{\infty} \frac{(-1)^n}{(2n + 1)!}

\sum_{n = 0}^{\infty} \frac{(-1)^n}{(4n + 2)(2n + 1)!}

\sum_{n = 0}^{\infty} \frac{(-1)^n}{(4n + 1)(2n + 1)!}