关键词: definite integral, indefinite integral, primary function

Abstract: Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f（x） is bounded and has primary function, the formal definite integral \int^x_s \tilde{f}（t）dt is the indefinite integral of f（x）, where x is a self-variable, s is a parameter,\tilde{f}（x） is a function defined in（-∞, +∞）, which comes from f（x） by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite. 

Key words: definite integral, indefinite integral, primary function