It is a confusing question.
Set $f:[0,+\infty)\to \mathbb{R}$ is a strictly convex downward function satisfy $$\lim _{x\to +\infty}\frac{f(x)}{x}=+\infty,$$ prove that $\int_0^\infty \sin f(x)dx$ is conditional convergence.
If $f$ has $C^1$ condition, it can use the Abel-Dirichlet Discriminance to solve. But it doesn't have this condition. I can't think of any way to solve it.