I am trying to evaluate the following integral. It has similarity to the Maclaurin expansion for $\sin$.
$$\int_{-\infty}^\infty{\sum_{n=0}^{\infty}\frac{(-1)^n}{\left(2n+x^2\right)!}}\text{dx}$$
- The $\sum$ is convergent for all $x$ using the ratio test.
- $\lim_{x\rightarrow\pm\infty}{\sum}=0$
- When $x=1$, the $\sum$ is equal to $\sin(1)$.