Integral of \( 3x^2 \) is \( x^3 \).
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- The \( n \)-th term of a geometric sequence is given by \( a_n = a_1 \cdot r^{n-1} \).
- So, \( a_6 = 3 \cdot 2^{6-1} = 3 \cdot 32 = 96 \).
- Evaluate the integral \( \int (3x^2 - 2x + 1) \, dx \).
- Integral of \( -2x \) is \( -x^2 \).
- Integral of \( 1 \) is \( x \).
- So, \( \int (3x^2 - 2x + 1) \, dx = x^3 - x^2 + x + C \), where \( C \) is the constant of integration.
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