Let $\displaystyle \ \ B(t,T):=\int_t^T f(t,s)ds$, where $f(.,.)$ is a stochastic process whose solution we don't know.
My lecture slides make the claim that:
$f(t,T) = \frac{\partial B(t,u)}{\partial u} \Bigg|_{u=T}$
My first question is, what's the notation $\frac{\partial .}{\partial.} \Bigg|_{u=T}$?
My second question is what is this notation?
$\frac{\partial B(t,T)}{\partial T} \Bigg|_{T\searrow t}$