1. Interpret the molarity

The solution is $2.6\times 10^{-3}\,\mathrm{M}$ in $\mathrm{CH_2Cl_2}$, i.e.

$2.6\times 10^{-3}\ \text{mol of DCM per litre of solution}$

Since the solvent volume given is $671.141\,\mathrm{mL}$ and the solute amount is very small, we take solution volume as approximately

$V = 671.141\,\mathrm{mL} = 0.671141\,\mathrm{L}$

So moles of $\mathrm{CH_2Cl_2}$ are

$n = M\times V = 2.6\times 10^{-3}\times 0.671141$

$n = 1.7449666\times 10^{-3}\,\mathrm{mol}$

2. Find mass of $\mathrm{CH_2Cl_2}$

Molar mass of $\mathrm{CH_2Cl_2}$:

$12 + 2(1) + 2(35.5) = 85\,\mathrm{g\,mol^{-1}}$

Hence,

$m_{\mathrm{DCM}} = n\times 85 = 1.7449666\times 10^{-3}\times 85$

$m_{\mathrm{DCM}} = 0.148322161\,\mathrm{g}$

3. Find mass of chloroform solvent

Given density of $\mathrm{CHCl_3}$:

$\rho = 1.49\,\mathrm{g\,cm^{-3}}$

Since $671.141\,\mathrm{mL} = 671.141\,\mathrm{cm^3}$,

$m_{\mathrm{CHCl_3}} = \rho V = 1.49\times 671.141$

$m_{\mathrm{CHCl_3}} = 1000.00009\,\mathrm{g} \approx 1000\,\mathrm{g}$

4. Calculate ppm by mass

For ppm by mass,

$\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}}\times 10^6$

Here,

$m_{\text{solution}} = 1000.00009 + 0.148322161 \approx 1000.1484\,\mathrm{g}$

Thus,

$\text{ppm} = \frac{0.148322161}{1000.1484}\times 10^6$

$\text{ppm} \approx 148.3$

So the required integer is

$\boxed{148}$

5. Comparison with stored answer

Stored correct answer = $148$.

This matches our derived answer.