Inverse Laplace Transform partial fraction $\frac {\frac{2S -1}{2}} {S^2-S+{\frac{5}{4}}} $

Question

Can anybody help me with the answer of this question?

Find the inverse Laplace transform of $$\frac {\frac{2S -1}{2}} {S^2-S+{\frac{5}{4}}} $$

Answer 1

Hint: Rewrite it as $$ \frac{\frac{2s-1}2}{s^2-s+\frac54}=\frac{(s-\frac12)}{(s-\frac12)^2+1}. $$