If `f(x)={{:(x+3 : x lt 3),(3x^(2)+1:xge3):}`, then find `int_(2)^(5) f(x) dx`.

Explanation

To solve the problem, we need to evaluate the definite integral of the piecewise function \( f(x) \) from 2 to 5. The function is defined as follows:

\[
f(x) =
\begin{cases}
x + 3 & \text{if } x < 3 \\
3x^2 + 1 & \text{if } x \geq 3
\end{cases}
...