Continunuity of the generalized primitive

Question

Let $f:I\subset \mathbb R\to \mathbb R$ be a Riemann locally integrable function on the interval $I$. Show that, for a fixed $a\in I$ $$ x\mapsto F(x) =\int_a^x f(t)dt ~~~~ $$ is continuous on $I$. This a claim in Brezis book's page 205 lemma 8.2