1. The problem is to evaluate the summation $$\sum_{i=3}^7 i$$. 2. The summation notation means we add all integers from the lower limit 3 to the upper limit 7 inclusive. 3. 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. 4. Here, $a_1 = 3$, $a_n = 7$, and $n = 7 - 3 + 1 = 5$. 5. Substitute these values into the formula: $$S = \frac{5}{2}(3 + 7)$$ 6. Simplify inside the parentheses: $$S = \frac{5}{2} \times 10$$ 7. Multiply: $$S = \frac{5 \times 10}{2}$$ 8. Cancel common factors: $$S = \frac{\cancel{5} \times 10}{\cancel{2} \times 1} = 5 \times 5 = 25$$ 9. Therefore, the sum of integers from 3 to 7 is 25.