Problem 1048 (difficulty: 2/10)

Let \(\displaystyle f\) be continuous, \(\displaystyle g(x)=\begin{cases} c & \text{if $x< {a+b \over 2}$} \\ d & \text{if $x> {a+b\over 2}$} \\ e & \text{if $x={a+b\over 2}$}\end{cases}\).

\(\displaystyle \int_a^b f\ dg=?\)

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