Let $f''(x)$ be continous and non zero on $[a,b]$ and if $f'(x)\geq m >0,~ \forall x,\in[a,b]$, prove that:
$\left|\int _a^b \sin(f(x))\,dx\right|\leq \frac{4}{m}$
Now, I need to use this theorem:
$\int_a^bf(x)g(x)\,dx=f(a)\int_a^cg(x)\,dx+f(b)\int_c^bg(x)\,dx$
There is also a hint that I should multiply the integrand by $\frac{f'(x)}{f'(x)}$.
I would be pleased if somebody could help me with directions, of how I should proceed?
Obviously, I should try to leave $f'(x)$ or $\frac{1}{f'(x)}$ in the integrand right? But if I try that I don't seem to get far. Maybe there is an intermediate step? Thanks!