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if you are integrating with respect to x, the indefinite integral of 1 is just x
The integral of 1 + x2 is x + 1/3 x3 + C.
The integral of a single term of a polynomial, in the form of AxN is (A/N+1) x (N+1).
The first integral of 2x is x2 + C.
The second integral of 2x is the first integral of x2 + C, which is 1/3x3 + Cx + C.
The integral of -x2 is -1/3 x3 .