Negative impulse from tension and weight integral

[nysnacc]

Homework Statement

Homework Equations

∫ F dt = mv

The Attempt at a Solution

I have
∫ T -mg dt
= ∫ 100+2t² - mg dt
= ∫ 100-9000*9.81 +2t² dt

but then I got negative impulse ...??

 

[haruspex]

T=100+2t²

... where the units are ...?

 

[nysnacc]

Oh I see 100+ 2t^2 in KN... mg should also in kN

 

[haruspex]

Oh I see 100+ 2t^2 in KN... mg should also in kN

Whatever makes all the units consistent.