1. The problem is to find the sum of the integers from 4 to 9 inclusive, which is written as $$\sum_{i=4}^{9} i$$. 2. The formula for the sum of an arithmetic series is $$S = \frac{n}{2}(a_1 + a_n)$$ where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. 3. Here, the first term $a_1 = 4$ and the last term $a_n = 9$. 4. Calculate the number of terms: $$n = 9 - 4 + 1 = 6$$. 5. Substitute into the formula: $$S = \frac{6}{2}(4 + 9)$$. 6. Simplify inside the parentheses: $$4 + 9 = 13$$. 7. So, $$S = 3 \times 13$$. 8. Multiply to get the sum: $$S = 39$$. 9. Therefore, the sum of the integers from 4 to 9 is 39.