AP Calculus: Functions defined by integrals

Question

Use the graph of f(t) = 2t + 4 on the interval [-4, 6] to write the function F(x), where F(x) = Int[2,x] f(t)dt

Answer 1

It isn't clear to me what the stated interval has to do with the problem.

 

f(t) is continuous on [-4,6] and the graph is a straight line.

 

F(x) = ∫₂^x (2t + 4)dt = (t² + 4t |₂^x = x²+ 4x - (4 + 8) = x² + 4x - 12

 

If I missed the point of the question, please send me a message.