Let $T,L> 0$ two real numbers and we consider the Sobolev space $X := L^2(0,T; H^1(0,L))\cap H^{1}(0,T;H^{-1}(0,L))$. My question is:

Given $f \in X$, the trace $ t \mapsto f(t,L)$ belongs to what space? Could someone indicate me a reference?