The integral of a function between two points is the area between its graph and the axis. For a rectangle that is width times height. A curve has no single height, so cut the interval into n strips and treat each strip as a rectangle.
Each rectangle is as wide as its strip and as tall as the function at one point of it, for instance at its left end. The sum of their areas is a Riemann sum. It is off by the small pieces between the rectangles and the curve.
Make the strips thinner and those pieces shrink. As n grows without end, the sums settle on one number: the integral.
The exact value here is 9. With 6 left rectangles the sum is 6.875; with 60 it is about 8.78. Each time n doubles, the error of a left sum roughly halves.
This is why integrating undoes differentiating: adding up many small changes of a quantity gives its total change. That link is the fundamental theorem of calculus.
Answer it first
A car's speed is recorded every second. How would you estimate the distance it travelled?
Show the answer
Multiply each speed by one second and add the results: a Riemann sum of speed over time. Shorter intervals give a better estimate.
Reading is not learning it
Leo teaches this at your pace, asks for your attempt before he shows his, and checks a week later what stayed.