Help with Calc please!

Question

Use the graph of f(t) = 2t + 2 on the interval [–1, 4] to write the function F(x), where .

Options:

1)	F(x) = x2 + 3x
2)	F(x) = x2 + 2x - 12
3)	F(x) = x2 + 2x - 3
4)	F(x) = x2 + 4x - 8

Answer 1

F(x) = ∫_{(from 1 to x)} [2t + 2]dt = (t² + 2t)_{(from 1 to x)} = (x² + 2x) - (1² + 2(1)) = x² + 2x - 3