To my best understanding, you're given that
[tex]\displaystyle\int_{C_1}\vec F\cdot\mathrm d\vec r=6\text{ and }\int_{C_2}\vec F\cdot\mathrm d\vec r=13[/tex]
where C₁ and C₂ are some arbitrary paths, evidently starting at the point P and ending at the point Q, and you have to find the value of
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r[/tex]
where C is the path consisting of C₁ (from P to Q) and the reverse of C₂ (from Q back to P). So we have
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{C_1}\vec F\cdot\mathrm d\vec r - \int_{C_2}\vec F\cdot\mathrm d\vec r = 6-13 = \boxed{-7}[/tex]
