For each function below, write a Riemann sum using $16$ rectangles to estimate the area under the curve over the interval $–4 ≤ x ≤ 4$. Then use your calculator to evaluate the sum. Recall that a Riemann sum does not have to involve sigma notation.

1. $g\left(x\right)=x\sin^2\left(x\right)$

   Hint (a):

   General form of a right endpoint Riemann sum:

   $f ( x ) = \left\{ \begin{array}{l}{ 3 \text { for } x < 0 }\\{ x ^ { 2 } + 3 \text { for } x \geq 0 }\end{array} \right.$

2. $f ( x ) = \left\{ \begin{array} { c } { 3 \text { for } x < 0 } \\ { x ^ { 2 } + 3 \text { for } x \geq 0 } \end{array} \right.$

   Hint (b):

   Your Riemann sum will need to split into two parts.

   Answer (b):

   $42.25$