The essay builds the integral upper limit function to obtaining other proof about theorem of integral first median value, and combine with theorem of calculus median value to proving Integral equality, inequality and median proposition.

• 通过构造积分上限函数,给出积分第一中值定理的另一证法,并结合微积分中值定理证明积分等式、积分不等式与定积分的中值命题。