# Help understanding proof of the fundamental theorem of calculus part 2

My calculus book has a proof of the fundamental theorem of calculus for continuous functions. I've been confused on one part though. How do they get the equation after "Thus, if $|h| < \delta$, we have"? I get that they just integrated the previous equation, but why does that follow because $|h| < \delta$ ?

• Because inequality in the previous equation only holds if $|t-x|<\delta$. – D Wiggles Jan 15 '14 at 19:53

Because inequality in the previous equation only holds if $|t−x|<\delta$. – IBWiglin Jan 15 at 19:53