Imagine you have a bunch of dots on a piece of paper. These dots are moving in different ways, some up and down, some left and right, some diagonal, and so on. An integral curve is a line that connects all of these dots that are moving in the same direction.
Let's say you have a dot that is moving straight up on the paper. You can draw an integral curve by connecting all of the dots that are also moving straight up. This line will show you the path that the dot is taking as it moves.
Integral curves can be used to understand how things are moving in different fields, like physics or engineering. They can help us to see patterns and predict where things will go in the future based on how they are currently moving.
So, integral curves are just lines that connect dots that are moving in the same direction, and they can help us understand movement in different fields.