Let 0< a < ß be real numbers. Let m > 2 be a natural number and let 0 < c1 < c2 < • ..< Cm < 1 be m points in the interval (0, 1). Define a function f on [0, 1] by f(x) = B if x = = Ck for some k=1,2,· .., m and f (x) = a if x + Ck for all k = 1,2, · . · , m. %3D Prove that f is integrable on [0, 1] and state the value of I f(x) dx.

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