1. The problem is to find the sum $S$ of integers from 1 to 100. 2. We recognize this as an arithmetic series where the first term $a_1=1$, the last term $a_n=100$, and the number of terms $n=100$. 3. The formula for the sum of an arithmetic series is $$S=\frac{n}{2}(a_1 + a_n)$$ 4. Substitute the known values: $$S=\frac{100}{2}(1 + 100)$$ 5. Simplify inside the parentheses: $$1 + 100=101$$ 6. Simplify the fraction: $$\frac{100}{2}=50$$ 7. Multiply to find the sum: $$50 \times 101 = 5050$$ 8. Therefore, the sum of the integers from 1 to 100 is $5050$.