1.
Let f(x)=∫0x(t+sin⁡(1−et))dtf(x) = \displaystyle \int_0^x \left(t + \sin(1 - e^t)\right) dt, x∈Rx \in \mathbb{R}. Then lim⁡x→0f(x)x3\displaystyle \lim_{x \to 0} \frac{f(x)}{x^3} is equal to