Problem
Let $V$ be the vector space of all polynomial functions $p$ from $\mathbb{R}$ to $\mathbb{R}$ which have degree two or less.
Define three linear functionals on $V$ by $f_1(p)=\int_0^1p(x)dx,\quad f_2(p)=\int_0^2p(x)dx , \quad f_3(p)=\int_0^{-1}p(x)dx.$
Show that $\{f_1,f_2,f_3\}$ is a basis for $V^{\ast}$, the dual space of $V$.
Progress
Very little so far...
I imagine the easiest way to approach this is to exhibit the set in $V$ to which $\{f_1,f_2,f_3\}$ is dual, and then to show it is a basis for $V$. Not sure how one would go about this however.
Any assistance would be appreciated. Regards.