The annual rate of coal production in the US (in billions of tons per year) is given by the function a(t), and the total amount of coal produced (in billion tons) since 1900 is given by c(t), where t represents years since 1900. If the total amount of coal produced is 27.5 billion tons higher in 1955 than it was in 1930. Required:
Write an integral to represent the 1997-2009 coal production.