Question: Let f : [ a , b ] R b e a n integrable function, and F ( x ) = a x f (

Let f:[a,b]Rbean integrable function, and F(x)=axf(t)dt.ByFTC-1,we know
that F'(x)=f(x). This exercise will examine what happens ifwe change the lower
bound of integration to some other number.
(a) For any cin[a,b], define Fc(x):=cxf(t)dt. Show that Fc(x)isan anti-derivative
off(x).
(b) From part (a), conclude that there exists a constant CinR such that F(x)=
Fc(x)+C. Determine the value ofC.
(c) Show that using Fc(x)in the statement ofFTC-2 give precisely the same result as
if one used F(x).
Let f : [ a , b ] R b e a n integrable function,

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