1. The problem asks: What is an integral used for? 2. An integral is a fundamental concept in calculus used to find the accumulation of quantities, such as areas under curves, total distance traveled, or accumulated change. 3. The main formula for a definite integral is: $$\int_a^b f(x)\,dx$$ which represents the area under the curve of the function $f(x)$ from $x=a$ to $x=b$. 4. Important rules: - The integral sums infinitely small slices $f(x)\,dx$ over the interval. - It can calculate areas, volumes, work done, and other accumulated quantities. 5. For example, if $f(x)$ is velocity, then the integral gives the total distance traveled. 6. In summary, integrals are used to calculate total accumulation of a quantity that changes continuously.