integral/continuety proof question..

[transgalactic]

function f(x) continues on [a,b]

suppose that for every sub part [math][\alpha ,\beta ]\subseteq [a,b][/math]

we have[math]\int_{\alpha}^{\beta}f(x)dx>0[/math].

prove that f(x)>=0 for [math] x\in[a,b] [/math]

 

if its wrong give a contradicting example??

 

 

i dont have a clue from here to start or how to go.

from the given i can conclude that if the sum of all subsections gives us a positive result then

the total sum from a to b has to positive too.inte