I am confused by the derivation in Srednicki QFT's chapter 6 from (6.8) to (6.9). In (6.8), we have
$$<q'',t''|q',t'>~=~\int DqDp \exp[i\int_{t'}^{t''}dt(p\dot{q}-H(p,q))],\tag{6.8}$$
and (6.9) we have
$$<q'',t''|q',t'>=\int Dq \exp[i\int_{t'}^{t''}dt L(\dot{q},q)].\tag{6.9}$$
It is clear for me that one can work out each infinitesimal integral $$<q_k|\exp[-i\delta t \frac{p^2}{2}]|q_{k-1}>~\sim~ \exp[\frac{i(q_k-q_{k-1})^2\delta t}{2}] $$ to derive the above formula. But I'm confused by the way that is presented in the book. It makes it sound like there is a more general way of computing path integral by finding the stationary point, i.e. given
$$\int Dp \exp[i\int f(p,t)dt]$$
is the result $$\exp[i\int F(t)dt]$$ where $F(t)=f(p(t),t)$ such that $p(t)$ is a stationary point of $f(p,t)$ with respect to $p$.
