Hello So I Had A Question If We Have A Piece Wise Probability Density Function F

hello so i had a question, if we have a piece-wise probability density function f(x) = { 1/25 if 0 < x < 5 , and 2/5 – 1/25x if 5 < x < 10.

to validate this pdf i integrated 1/25 from 0 to 5 i got 1/5 and then i integrated 2/5-1/25x from 5 to 10 and i got 1/2

when summing both i dont get 1 ?? can you explain how to validate this pmf function and then find the cdf