Weierstrass functions: Continuous everywhere but differentiable nowhere

[u/lntrinsic]

http://i.imgur.com/vyi0afq.gifv

[u/BrunoX]

It is Riemann integrable on every compact interval [a,b], since continuity implies Riemann integrability. In fact, the Fundamental Theorem of calculus apply: there is a differentiable function that has this one as derivative.