I wanted to ask this 1 questions because i didn't even know where to start.

Question

For a continuous function f(x), f(1) = 11, and Integral symbol from 1 to 5 f'(x)dx=9. Find f(5).

Answer 1

draw a graph
point A is (1/11)

f(5) = f(1) + integral 1 to 5 (f' dx)
= 11 + 9
= 20

or just say
integral from 1 to 5 of (dy/dx) dx
= y(5)-y(1)