2. Prove or disprove these two statements: (i) if ƒ is Riemann integrable on [a, b] then so is |ƒ|. (ii) if f is Riemann integrable on [a, b] then so is f. (Hint: Try a slight modification of the Dirichlet function as a potential counterexample).

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A: Please refer the attached image for complete solution.

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A: Introduction:   "A vector field                     F =P(x, y, z), Q(x, y, z), R(x, y, z)      is…