Early uni/college Calculus (one question)

Attatched question pic below. Answer doesn't have to be long, can be somewhat middle of short n long, but precise or straight to the point with the working. Thank you.

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  • comment: upon reading the answer again I note that I made a miscalculation. In the third equation one should get f(\pi) * (1) - f(0) * (-1) instead of f(\pi) *(-1) - f(0)*(-1) - as cos(\pi)=-1 not 1. This should then enter into the second to last equation where you get 4 = f(0) + 9, the solution then becomes f(0)= 4-9 = -5.

  • Unfortunately it is not possible to edit answers once they are submitted, which is why I must put the correction in a comment instead.

  • Yes that is all good, thanks so much for your help!

The answer is accepted.