Let the function $f ( x ) = \left\{ \begin{array} { l l l } x ^ { 2 } - 6 x + 11 & \text { if } & x < 2 \\ \sqrt { 5 x - 1 } & \text { if } & x \geq 2 \end{array} \right.$. a) ( 0.5 points) Study the continuity of the function in $\mathbb { R }$. b) (1 point) Study the relative extrema of the function in the interval ( 1,3 ). c) (1 point) Calculate the area enclosed by the function and the $x$-axis between $x = 1$ and $x = 3$.