# Integration constant question

by wumple
Tags: constant, integration
 P: 60 Hi, I thought that if you integrate with limits, you don't include a constant, but if you don't integrate with limits (indefinite), there is a constant. But my book gives the example (all functions are single variable functions, initially of x but then changed to s for the integration): $$f' = \frac{1}{2}(\phi'+\frac{\psi}{c})$$ Integrating: $$f(s) = \frac{1}{2}\phi(s) + \frac{1}{2c}\int_0^s\psi + A$$ What's going on here?