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Given that f(x)=3x26x+1 and f(3) = 5, fi...

Given that f(x)=3x26x+1 and f(3) = 5, find f(x).

A.

f(x)=x33x2+x+20

B.

f(x)=x33x2+x+31

C.

f(x)=x33x2+x+2

D.

f(x)=x33x2+x13

Correct answer is C

f(x)=3x26x+1

f(x)=(3x26x+1)dx

= x33x2+x+c

f(3)=5=333(32)+3+c

2727+3+c=53+c=5

c=2

f(x)=x33x2+x+2