I have a functional $f: L^2[-1,1]\to\mathbb{C}$, how do I find a $v$ such that $f(x)=\langle x,v\rangle$ for all $x$? Since $L^2$ is a Hilbert space, I know the Riesz Representation theorem holds but I'm not sure what form $v$ is supposed to take... The functional is
$$ f(x) = i\int_{-1}^{1} x(t) dt + \int_{0}^{1} tx(t)dt $$
Thanks