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

suppose that for every sub part $\displaystyle [\alpha ,\beta ]\subseteq [a,b]$

we have$\displaystyle \int_{\alpha}^{\beta}f(x)dx>0$.

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

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