here I have a PDE equation and the initial value,and by pdsolve(PDE,IBC,time=t,range=.....) I get the expression of the  numerical solution as pds.

eg

PDE:=diff(p,t)+diff(p,a)=-up;

IBC:={p(a,0)=sina,p(0,t)=cost}

pds:=pdsolve(PDE,IBC,numeric,time=t,range=0..2); 

Then how can I integrate p(a,T) for a from 0 to 10(here t is fixed to be T); how can I use the pds and the concrete peocedure is ?              many thanks!