5. The continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\) given by
$$f ( x ) = \left\{ \begin{array} { c c }
k \left( x ^ { 2 } + a \right) & - 1 < x \leqslant 2
3 k & 2 < x \leqslant 3
0 & \text { otherwise }
\end{array} \right.$$
where \(k\) and \(a\) are constants.
Given that \(\mathrm { E } ( X ) = \frac { 17 } { 12 }\)
- find the value of \(k\) and the value of \(a\)
- Write down the mode of \(X\)