% Preview source code from paragraph 0 to 12x a<x<a+

there is integrabile function f in {[}a,b{]} so f(a)<0.

f is continues from the right of a.

prove that there is so

prove:

there is from the given continuety

in a there is a delta

so for every x in which .

so and the ({*})

f is integrabile in [a,b] and so in [a,a+ ]

from ({*}) and from the monotonicity we conclude

.

i got stuck on the first step:

why they chose such delta and x??

from the defintion it should be there is delta>0 for which in every