$f$ and $g$ are two differentiable functions on the real line such that $f$ is strictly increasing and $g$ is strictly decreasing. Define $p(x)=f(g(x))$ and $q(x)=g(f(x))$ for all real number $x$. Then for $t>0$ the sign of $$\int_0^t p'(x)(q'(x)-3)dx$$ is
a)positive
b)negative
c)dependent on $t$
d)dependent on $f$ and $g$.
I am taking particular examples for $f$ and $g$ such as $f(x)=x$ and $g(x)=-x$, the results are all positive but cannot find out the general result for all functions having those specified properties.