Choosing correct DAC: DNL and INL
Regarding the DNL and INL of a DAC, DNL is the error difference
  between actual step width and ideal value (1 LSB). INL is the
  deviation of actual transfer function from the shown straight line
  (Shown in image below).


I think you have them backwards. I find it easier to look at the equations.

Differential NonLinearity means the difference between the voltage measured on the previous bit vs the bit your looking at now. It is simply a comparison between bits. You are correct in that the DNL needs to be under one to be monotonic. Higher DNL means less glitches in a continuous waveform generation such as a sine wave. 


Source: Wikipedia DNL

Integral NonLinearity means from the current value \$ V_{D}\$ to the zero point \$ V_{Zero}\$ (which makes a straight line, and the whole equation forms a variant of y=mx+b or line equation) , and is an absolute measure, If you pick a DAC with lower INL than 1, it will be within 1LSB of the value that you would expect from bottom of the DAC range. INL is for DC or precision applications and knowing exactly what the DAC output is. 

$$INL =  [\frac{V_D - V_{ZERO}}{V_{LSB-IDEAL}}] - D  \space , where \space 0 &lt; D &lt; 2N-1.$$