Approximate $$$\int\limits_{1}^{7} f{\left(x \right)}\, dx$$$ with the Riemann sum using the table $$$\left[\begin{array}{ccccccc}1 & 2 & 3 & 4 & 5 & 6 & 7\\4 & -2 & 3 & 1 & 0 & 5 & 9\end{array}\right]$$$

Approximate the integral $$$\int\limits_{1}^{7} f{\left(x \right)}\, dx$$$ with the left Riemann sum using the table below:

The left Riemann sum approximates the integral using left endpoints: $$$\int\limits_{a}^{b} f{\left(x \right)}\, dx\approx \sum_{i=1}^{n - 1} \left(x_{i+1} - x_{i}\right) f{\left(x_{i} \right)}$$$, where $$$n$$$ is the number of points.

Therefore, $$$\int\limits_{1}^{7} f{\left(x \right)}\, dx\approx \left(2 - 1\right) 4 + \left(3 - 2\right) \left(-2\right) + \left(4 - 3\right) 3 + \left(5 - 4\right) 1 + \left(6 - 5\right) 0 + \left(7 - 6\right) 5 = 11.$$$

$$$\int\limits_{1}^{7} f{\left(x \right)}\, dx\approx 11$$$A