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Let f be a real valued function defined ...

Let f be a real valued function defined on R (the set of all real numbers) such that `f(1) = f(-1) = 5` and whose graph of f is symmetrical with respect to the lines `x=+-1.` Given `sum_(r=50)^99 f(r/100) and sum_(r=50)^99 f((-r)/100)=5.` If `S=sum_(r=50)^150 f(r/100)+sum_(r=50)^150 f((-r)/100).` Then find S.

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