Muon-spin-rotation measurements of the London penetration depths in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">YBa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>6.97</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Muon-spin-rotation (\ensuremath{\mu}SR) experiments on a high-quality sintered ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ sample [x=6.970(1)] were performed, in order to obtain an accurate knowledge of the magnitude and the temperature dependence of the magnetic penetration depth in this copper oxide superconductor. Special attention was given to the data analysis. In particular, the systematic errors introduced by different types of analyses were estimated. Our results show that the temperature dependence of the effective penetration depth ${\ensuremath{\lambda}}_{\mathrm{eff}}$ into the sintered sample is well described by the two-fluid model, with ${\ensuremath{\lambda}}_{\mathrm{eff}}$(0)=155(10) nm. This behavior of ${\ensuremath{\lambda}}_{\mathrm{eff}}$(T) is consistent with conventional s-wave pairing. With the anisotropy ratio \ensuremath{\gamma}=${\ensuremath{\lambda}}_{\mathit{c}}$/${\ensuremath{\lambda}}_{\mathit{a}\mathit{b}}$=5(1) measured in a previous \ensuremath{\mu}SR experiment, the penetration depths ${\ensuremath{\lambda}}_{\mathit{a}\mathit{b}}$(0)=130(10) nm and ${\ensuremath{\lambda}}_{\mathit{c}}$(0)=500--800 nm (parallel and perpendicular to the ${\mathrm{CuO}}_{2}$ planes, respectively) were extracted. Our results are compared with those obtained by other experimental techniques and theoretical predictions.