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Home page > Section in English > The Riemann Integral > Fundamental theorem of the integral calculus > Continuity of the integral function

Continuity of the integral function

The proof is a simple consequence of the mean value thoerem. If , consider a point d. We have: , where is a number between the inf and the sup of f in [d,x] (or [x,d]). Then as x tends towards d, the last member tends to zero (due to the fact that f is bounded). This proves continuity of F.

Home page > Section in English > The Riemann Integral > Fundamental theorem of the integral calculus > Continuity of the integral function

first published on january 07 2003 - last updated on september 01 2003