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Please correct me where I'm wrong.

(imaginary question)

Suppose you have a mass distribution across a line, where the mass of each point is given by the equation f(x)=a*x (assume a is a constant)

find the total mass, if the line is c meters long (beggining @ x=0)

(My stupid train of thought)

We have to add up all the individual masses on the line.

so divide the line into n segments, calculate the mass for each one and add them up

f(x1)+f(x2)+...+f(xn)=

a*x1+a*x2+...+a*xn=

a(x1+x2+...+xn)=

a*c

What am i doing wrong?

(Besides the language use, I'm not a native and have little experience in such teminology)