Question

suppose

x
S f(t) dt= x^2 - 2x + 1. Find f(x).
1

S = integral and 1 = lower level, x = upper

i don't understand what i'm supposed to find/what to do

Answer 1

did you mean "Find f(t)" ?

let f(t) = at^2 + bt + c

then the integral of f(t) by dt from t = 1 to t = x
= ax^2 + bx + c - (a + b + c)
= ax^1 + bx - a - b

comparing this with x^2 - 2x + 1 gives
a=1
b=-2 and
-a -b = 1 This last equation is true,
and c could be anything

so f(t) = t^2 - 2t + c