I'm asked to show the following:
"If $f\in \bf{R}$ $[a,b], $ then $ \displaystyle\int_{a}^{b} f = \lim_{c \to a^{+}} \int_{c}^{b} f$.
Here, $\bf{R}$ stands for the set of Riemann integrable functions over the set $[a,b]$.
I'm not sure where to really go with this except making use of the definitions of a Riemann integrable function;
$|U(P,f)-L(P,f)|<\epsilon$ for some partition P,
$|S(P,f)-\int_{a}^{b} f| < \epsilon$ provided that $||P|| <\delta$
I'm not sure how to work the $\displaystyle \lim_{c\to a^+}$ into the inequalities.
Any hints/tips would be appreciated! Thanks.