Let f(x) = 3x^2 -2 to find the following value  F(t+1) =?

f(x) = 3x^2 - 2

f(t + 1) = 3t^2 + 6t + 1

:-

f (t + 1) = 3 ( t + 1 )² - 2

f (t + 1) = 3 (t² + 2t + 1) - 2

f (t + 1) = 3 t² + 6t + 1

// Are you looking for the antiderivative F(t+1) or are you looking for f(t+1) ???

// If you're looking for the ANTIDERAVITAVE

Given f(x) = 3x²-2, the antiderivative of f(x) is

.....F(x) = x³-2x+C

ans

.....F(t+1) = (t+1)³ - 2(t+1) + C

.....F(t+1) = t³+1+3t(t+1)+C...............ANS

// If you're simply looking for f(t+1),

f(t+1) = 3(t+1)² - 2

.........= 3t²+6t+3 - 2

.........= 3t²+6t+1............................ANS

Simply replace x by t+1 and calculate:

3(t+1)^2 -2 

=> 3t^2 +6t + 3 -2

=> 3t^2 +6t + 1

=> 3t(t+2) + 1