can it be a distrubution function?

Hi,
this week's HW had this distribution function

f =
1-(3/4)exp(-x) x >= 0
0 otherwise

then I was asked to compute P(0 <= x <= 2). if i understand correctly,
i need to compute the integral of f(x) at the given interval. as a
preliminary stage i tried to compute the integral of f on the entire
sample space. i expected it to be 1. what i got was:

(integral)[0,+inf](1-(3/4)exp(-x)) = (x + (3/4)exp(-x)) between 0 and
+inf = inf !

this integral does not converge, because of the "x". so, am i doing
something wrong or that f cannot be a distribution function ?

thanks

.

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