Additivity Integration Problem

[rrrright]

Homework Statement

View attachment latex-image-1.pdf equals...

Homework Equations

\int_a^{b} f(x)dx+\int_b^{c} f(x)dx=\int_a^{c} f(x)dx

\int_b^{a} f(x)dx=-\int_a^{b} f(x)dx

The Attempt at a Solution

View attachment latex-image-1.pdf

View attachment latex-image-2.pdf

\int_2^{-1} f(x)dx-\int_2^{5} f(x)dx

\int_2^{-1} f(x)dx+\int_5^{2} f(x)dx

\int_5^{-1} f(x)dx

The answer key says the answer is View attachment latex-image-3.pdf Where did i go wrong?

 

[Mark44]

Homework Statement

View attachment 30603 equals...

Homework Equations

\int_a^{b} f(x)dx+\int_b^{c} f(x)dx=\int_a^{c} f(x)dx

\int_b^{a} f(x)dx=-\int_a^{b} f(x)dx

The Attempt at a Solution

View attachment 30603

View attachment 30604

\int_2^{-1} f(x)dx-\int_2^{5} f(x)dx

\int_2^{-1} f(x)dx+\int_5^{2} f(x)dx

\int_5^{-1} f(x)dx

The answer key says the answer is View attachment 30605 Where did i go wrong?

I get
-\int_{-1}^{5} f(x)dx
which is the same as what you got. It looks to me like the answer key is missing the - sign out front.