JEE Math Practice Question

Let $$f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}$$. Then, $$\lim \limits_{x \rightarrow 0} \frac{f(x)}{x^3}$$ is equal to

1. A.$$\frac{1}{6}$$
2. B.$$-\frac{1}{6}$$
3. C.$$\frac{2}{3}$$
4. D.$$-\frac{2}{3}$$