Integral of a positive function is positive? Question:
Let $f:[a.b]\to \Bbb R \in R[a,b]$ s.t. $f(x)>0 \  
\forall x \in \Bbb R.$ Is $\int _a^b f(x)\,dx>0$ ?
What We thought:
We know how to prove it for weak inequality, for strong inequality - no clue :-) 

If f is continuous, we can argue like this, Let $m$ be the infemum of the function on$[a,b]$. show that $m \gt 0$ and $\int _a^b f(x)\,dx \gt m(b-a) \gt 0$
