What is an integral?

An integral is the area that lies below a graphed line and the x-axis, an indefinite integral is when an interval is not used, and so is often infinite, as it covers the entire area under a graph, and not just a small section.
When an interval is used, the integral will usually be finite, e.g.
The integral of x between 0 and 2 is equal to [x²/2]²₀  which is equal to 2²/2-0²/2=2
If you think of this as the line y=x, and simply take the line from x=0 to x=2, then you can see that the graph forms a right angled triangle with base and height 2, calculate the area and you can see that it is also equal to 2, as expected.