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Assuming you specifically mean calculus an integral is basically the area between some graph and the x-axis between two points. Imagine this:
You have a graph with a line on it (doesn't matter if it's a line or a curve or anything, so long as it doesn't loop back on itself, for now, you have a straight line). Now, pick two places on the x-axis to put vertical lines (these are the boundaries you'll work in). Now you have a left boundary, a right boundary, and a top and bottom boundary (the x axis is one and the line is the other). So, you have a 2-d closed shape. The area this shape covers is the integral of that line from a to b. Above the axis is positive and below the axis is negative.
I'll link to a few pictures to help visualize it. In each one there will be an "a" on the left, a 'b' on the right, some graph and the x-axis. Those are the boundaries and the area inside those boundaries is the integral.
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