What does the free number C mean in the integral?

Question

higher mathematics

If we take the usual integral over x from a to b, which can be depicted as a graph as a closed figure, then what does it mean and how to freely display the number C? What is it for and how is it used in practice?

Answer 1

For an indefinite integral, the letter C denotes any number (constant). For understanding, take y = x**2, y = x**2 +2, y = x**2 - 2. Find the derivative. And now, from these derivatives, calculate the integral back. As you can see, the constant is lost, so you need to add it to the answer. Used only in the indefinite integral