Area under waveform in t-domain including 2 delta functions
please someone confirm if following  devlopment is right or  wrong .becuase answer of exercise question isn't provided in book "F F kuo"

we know 

$f(t)\xrightarrow{\mathcal{F}}F(j\omega); $ where, $F(j\omega) =\displaystyle\int_{-\infty}^{\infty} f(t) \ e^{-j\omega t} \ dt\implies F(0)=\text{area under time domain curve }$ 

So, $(a)\ F(j\omega)=2+T.\ Sa{(\omega T/2)}+Ke^{-j\omega T}\implies F(0)=2+T+K=\displaystyle\int_{-\infty}^{\infty}f(t)dt$

but area is given zero therefore , $K=-(2+T)$ . 

and it is resonable also becuase strength of impulse at $t=T$ must be equal to the negative summation of  area of regions preceding it. 

similarly,

for part $(b)\ $   $K=-T$ because time is starting from $t=0_{+}$ that's why excluding impulse of strength  $2$ at $t=0$

note :

$Sa (\omega T/2)=\dfrac{\sin\left(\dfrac{\omega T}{2}\right)}{\omega T/2}$