Answer
a) False b) False c) True
Work Step by Step
Differentiate each option to check the original integral:
a) We have: $\dfrac{d}{dx}[\dfrac{(2x+1)^3}{3} +C]=\dfrac{1}{3}(3 (2x+1)^2)(2)\ne (2x+1)^2$
b) We have: $\dfrac{d}{dx}[(2x+1)^3 +C]=(3 (2x+1)^2)(2)\ne
3(2x+1)^2$
b) We have: $\dfrac{d}{dx}[(2x+1)^3 +C]=(3 (2x+1)^2)(2) =6(2x+1)^2$
Hence, a) False, b) False, c) True