Given the vector space $\begin{equation} \text{P}_2[t] = \{ a + b\,\, t + c \,\,t^2 \mid a, b, c \in \mathbb R\,\,\,\, \} \end{equation}$ and linear functionals $\phi_1, \phi_2, \phi_3 \in \left( \text{P}_2[t] \right) ^* $ defined as below;
$ \begin{equation} \phi_1\left(\,\,p\,\,\left(\,\,t\right)\,\,\right) = \int_0^1 \! p\,\,\left(\,\,t\,\,\right)\,\,\mathrm{d}t \end{equation}$
\begin{equation} \phi_2\left(\,\,p\,\,\left(\,\,t\right)\,\,\right) = p\,\,\,\,^'\,\,\left(\,\,1\right) \end{equation}
$\begin{equation} \phi_3\left(\,\,p\,\,\left(\,\,t\right)\,\,\right) = p\,\,\left(\,\,0\right) \end{equation}$
Show that $\beta^* = \{ \phi_1, \phi_2, \phi_3 \}$ is linearly independent. And determine the $\beta\,\,\,\,\,$ base which has the dual base $\beta^*$.
I really don't know how to proceed with this question, any help would be appreciated.