The World API provides the user with access to data from the past 7 days ("Live" data) and predictions of what is likely to occur over the next 7 days ("Forecast" data). Each have separate API endpoints.
For Solar Radiation Forecasts:
For Solar Radiation Live data:
For your locations of interest, the API Toolkit provides a snapshot of the data from these two endpoints, for the current day. These are separated by the vertical dotted line 'Now', with the solid grey line showing the most recent Live data for the location, and the orange line showing the median forecast (shading indicated the 10th and 90th percentile of probability).
These preview graphs will update (via page refresh) with every Rapid Update Cycle. They only contain the most recent Live data and the Forecast data from the current day. The API itself will provide -7 days through to +7 day (Live and Forecast data, respectively).