Find the specified area. The area under the graph of $f$ over the interval $[-1,4]$ \[ f(x)=\left\{\begin{array}{c} 3, \text { if } x<1 \\ 3 x^{2}, \text { if } x \geq 1 \end{array}\right. \] A. 69 B. $\frac{256}{3}$ C. 15 D. 195

Step 1 ：The function is piecewise defined, so we need to split the integral into two parts: one for the interval [-1, 1] where the function is defined as 3, and one for the interval [1, 4] where the function is defined as \(3x^2\).

Step 2 ：First, calculate the area under the graph from -1 to 1. The function is constant and equal to 3 in this interval, so the area is simply the length of the interval times the function value, which is \((1 - (-1)) * 3 = 6\).

Step 3 ：Next, calculate the area under the graph from 1 to 4. The function is \(3x^2\) in this interval, so the area is the integral of \(3x^2\) from 1 to 4, which is \(\left[ x^3 \right]_1^4 = 4^3 - 1^3 = 63\).

Step 4 ：Finally, add the two areas together to get the total area under the graph from -1 to 4, which is \(6 + 63 = 69\).

Step 5 ：Final Answer: The area under the graph of the function over the interval [-1,4] is \(\boxed{69}\).