Use a limit of Riemann sums to evaluate the definite integral.
\[
\begin{aligned}
\int_{3}^{5}(4 x-1) d x & =\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \\
& =\lim _{n \rightarrow \infty} \\
& =
\end{aligned}
\]

Hint: This list of summation rules may be helpful.

Answer

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Answer

The final answer is \(\boxed{30}\)

Steps

Step 1 ：Set up the Riemann sum for the function \( f(x) = 4x - 1 \) over the interval \([3, 5]\)

Step 2 ：Use the limit definition of the definite integral, taking the limit as \( n \) approaches infinity of the sum of \( f(x_i) \times \Delta x \)

Step 3 ：Use the right endpoint of each subinterval as the sample point

Step 4 ：Calculate the definite integral using the limit of Riemann sums

Step 5 ：The final answer is \(\boxed{30}\)