Example If X is a continuous RV with PDF given by: 0 x < 0 f(x) = х 2 ; 0 < x < 2 : x > 2 i. = 00 ii. = Find F(x) and dr

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I don't know how to define the limits of integration? This confuses me in CDF, and the X in the limits of integration is very confusing
The third step of the solution iii in red, how did the output become 1? Also, not all terms of integration contain x like the rest of the steps? How is that
And also in green, is it always the same value? I mean, should x always be less than a number with a probability of zero and x is greater than a number with a probability of 1??
Please explain
If you use handwriting please make it clear
Example If X is a continuous RV with PDF given by: 0 x < 0 f(x) = х 2 ; 0 < x < 2 : x > 2 i. = 00 ii. = Find F(x) and draw it. x < 0: F(x) = f*. f(t)dt = $. *Odt = 0 0 SX S2: F(x) = {* f(t)dt = f(t)dt + So f(t)dt so ſode + fedt = 0 + (8) x > 2: F(x) = S . f (t)dt = f (t)dt + S3 f(t)dt + $* f(t)dt od + Dsde + out = 0 + (x + = -1 S* ) * = x2 Odt X 1 29 1t2 + lo 2 = 2 1 tdt + 1/t2 Odt 0 + 0 = - = F(x) 0.5 -00 0 1 F(x) = 2 x < 0 ; 0<x< 2 3 x > 2 0 0 2. X