The function $y = x^{2} + 3x - 4$ intersects the x-axis at $\left ( 1,0 \right )$
We will take only first quadrant into consideration. So, the intersection point of the given equation and the line $x = 5$ is the point $\left ( 5,36 \right )$. (put $x = 5$ in the quadratic equation and $y$ turns out be 36).
So, the answer to this question is the area under the curve of the given equation and the line $x = 5$ i.e. from $x = 1$ to $x = 5$ .
This can easily be calculated using integration.
$\int_{1}^{5} x^{2} + 3x - 4$ $dx$ = $\frac{368}{6}$ = $61 \frac{1}{3}$
Option B is the correct answer.