Anti-differentiation or integration is the reverse process to differentiation. For example, if f 0 (x) = 2x, we know that this is the derivative of f(x) = x^2 . Could there be any other possible answers? 

If we shift the parabola f(x) = x^2 by sliding it up or down vertically, all the points on the curve will still have the same tangent slopes, i.e. derivatives. 

Example on the right : All have the same derivative function, y' = 2x, so a general expression for this family of curves would be y = x^2 + c where c is an arbitrary constant (called the integration constant).