Checkpoint 1

Suppose ${\displaystyle f}$ is any continuous function on the interval ${\displaystyle [a,b]}$. Explain why ${\displaystyle {\int }_a^{b}f\text{(}t\text{)} dt=F\text{(}b\text{)}}$, where ${\displaystyle F\text{(}t\text{)}}$ is the solution of the initial value problem

${\displaystyle \frac{dF}{dt}=f\text{(}t\text{)}}$,    ${\displaystyle F\text{(}a\text{)}=0}$.